Part 2 of 5:
Free Riding and Vote Management
under Proportional Representation
by the Single Transferable Vote
(draft, 14 March 2011)
Markus Schulze
[email protected]
Abstract. We give an overview over free riding strategies and vote
management strategies under proportional representation by the single
transferable vote (STV). A free rider is a voter who does not waste his vote
by voting for a candidate who is certain to be elected even without one’s
vote. Vote management is a strategy where a party maximizes its number of
seats by asking its supporters to vote preferably for those of its candidates
who are less assured of election. We demonstrate that these strategies are a
common feature of everyday political life wherever STV methods are being
used. Furthermore, we demonstrate that there are mainly only two types of
free riding strategies, but a very large and colorful family of vote
management strategies. We will introduce a mathematical model to describe
free riding and vote management and we will introduce an STV method that
is vulnerable to these strategies only in those situations in with otherwise
Droop proportionality would have to be violated.
JEL Classification Number: D71
This paper is the second part of a series of papers that can be downloaded here:
http://m-schulze.webhop.net/schulze1.pdf
http://m-schulze.webhop.net/schulze2.pdf
http://m-schulze.webhop.net/schulze3.zip
http://m-schulze.webhop.net/schulze4.pdf
http://m-schulze.webhop.net/schulze5.pdf
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Contents
1. Introduction ............................................................................................ 3
2. Basic Definitions ..................................................................................... 4
3. Free Riding ............................................................................................. 6
3.1. Woodall Free Riding .................................................................. 7
3.2. Hylland Free Riding ................................................................. 15
3.3. Summary .................................................................................. 16
4. Vote Management ................................................................................. 17
4.1. Some Examples ........................................................................ 17
4.2. Equalizing of First Preferences and Later Preferences ............... 23
4.3. Number of Candidates .............................................................. 23
4.4. Criteria ..................................................................................... 25
4.5. Strictness .................................................................................. 27
4.6. Symmetry ................................................................................. 28
4.7. Summary .................................................................................. 31
5. Proportional Completion ....................................................................... 32
5.1. Definition of Proportional Completion ...................................... 33
6. A New STV Method ............................................................................. 34
6.1. Equivalence of Free Riding and Vote Management ................... 34
6.2. Definition of the Schulze STV Method ..................................... 37
6.3. Example ................................................................................... 38
7. Proportional Rankings ........................................................................... 42
7.1. Definition of the Schulze Proportional Ranking Method ........... 44
7.2. Example ................................................................................... 46
8. Database ............................................................................................... 49
9. Conclusions .......................................................................................... 50
References ................................................................................................ 50
2
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
1. Introduction
When STV methods are criticized, then they are usually criticized for
violating monotonicity, participation or consistency (Brams, 1984; Doron,
1977; Dummett, 1984, 1997; Nurmi, 1997; Saari, 1994). However, we are
not aware of any instance where a violation of these criteria has actually
been misused for strategic purposes. In this paper, we demonstrate that rather
free riding (section 3) and vote management (section 4) are the two most
serious problems of STV methods.
A free rider is a voter who misuses the fact that in multi-winner elections
it is a useful strategy not to vote for a candidate who will be elected even
without one’s vote. Free riders are frequently used as an explanation why in
multi-winner elections popular candidates get fewer votes resp. fewer first
preferences than their popularity suggests (Hatton, 1920). But, to the best of
our knowledge, there is not yet any empirical study about whether free riding
strategies are really causal for this observation and about how many voters
actually use free riding strategies. However in section 3 of this paper, we use
the ballot data of the City Council and School Committee elections in
Cambridge, Massachusetts, to determine the number of voters who use a free
riding strategy that has been predicted e.g. by Woodall (1983) and Tideman
(2000) (Woodall free riding). We do not find any evidence at all that voters
use this free riding strategy. We give explanations why voters do not use this
strategy (Hylland free riding; possible backfire of Woodall free riding;
Woodall cannot be misused by political parties on a larger scale; etc.).
Vote management is a strategy where a party or a group of independent
candidates maximizes its number of seats by spreading its votes evenly
among its candidates. It has already been predicted by Droop (1881) that
vote management is a useful strategy under STV with the Andrae-Hare
quota. The term “vote management” is used in this manner since about 1987
(Mair, 1987a, 1987b). Since the mid-1990s, it is accepted that vote
management is a useful strategy also under STV with the Droop quota
(Gallagher, 1993b, 2003; Marsh, 1999).
We will introduce a theoretical concept to describe vote management
(section 6.1). This concept will be used to introduce an STV method that is
vulnerable to free riding and vote management only in those cases in which
otherwise Droop proportionality would have to be violated (section 6.2).
Furthermore, this concept will be used to introduce a method to produce
party lists (section 7).
3
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
2. Basic Definitions
We presume that A is a finite and non-empty set of candidates. C ∈ 
with 1 < C < ∞ is the number of candidates in A.
A binary relation  on A is asymmetric if it has the following property:
∀ a,b ∈ A, exactly one of the following three statements is valid:
1.
2.
3.
a  b.
b  a.
a ≈ b (where “a ≈ b” means “neither a  b nor b  a”).
A binary relation  on A is irreflexive if it has the following property:
∀ a ∈ A: a ≈ a.
A binary relation  on A is transitive if it has the following property:
∀ a,b,c ∈ A: ( a  b and b  c ⇒ a  c ).
A binary relation  on A is negatively transitive if it has the following
property (where “a  b” means “not b  a”):
∀ a,b,c ∈ A: ( a  b and b  c ⇒ a  c ).
A binary relation  on A is linear if it has the following property:
∀ a,b ∈ A: ( b ∈ A \ {a} ⇒ a  b or b  a ).
A strict partial order is an asymmetric, irreflexive, and transitive relation.
A strict weak order is a strict partial order that is also negatively transitive.
A linear order is a strict weak order that is also linear.
A profile is a finite and non-empty list of strict weak orders each on A.
N ∈  with 0 < N < ∞ is the number of strict weak orders in V : = { 1, ...,
N }. These strict weak orders will sometimes be called “voters” or
“ballots”.
“a v b” means “voter v ∈ V strictly prefers candidate a ∈ A to candidate
b”. “a ≈v b” means “voter v ∈ V is indifferent between candidate a and
candidate b”. “a v b” means “a v b or a ≈v b”.
A possible implementation of the Schulze method looks as follows:
Each voter gets a complete list of all candidates and ranks these
candidates in order of preference. The individual voter may give the
same preference to more than one candidate and he may keep
candidates unranked. When a given voter does not rank all candidates,
then this means (1) that this voter strictly prefers all ranked candidates
to all not ranked candidates and (2) that this voter is indifferent
between all not ranked candidates.
4
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
M ∈  with 0 < M < C is the number of seats.
AM is the set of the (C!)/((M!)·((C–M)!)) possible ways to choose M
different candidates from the set A. The elements of AM are indicated with
wedding letters A, B, C, ....
D : = N/(M+1) is the so-called Droop quota.
H : = N/M is the so-called Andrae-Hare quota.
Suppose there is a set of candidates ∅ ≠ B ⊊ A such that more than s ∈ 
Droop quotas of voters prefer each candidate b ∈ B to each candidate a ∉ B.
Then Droop proportionality says that at least min { s, |B| } candidates of this
set must be elected, where |B| is the number of candidates in B.
Suppose there is a set of candidates ∅ ≠ B ⊊ A such that at least s ∈ 
Andrae-Hare quotas of voters prefer each candidate b ∈ B to each candidate
a ∉ B. Then Andrae-Hare proportionality says that at least min { s, |B| }
candidates of this set must be elected.
Droop proportionality implies Andrae-Hare proportionality.
Proportional representation by the single transferable vote (STV) is an
election method to fill M seats with the following properties:
(1) Input of this method is a profile V.
(2) Output of this method is a set ∅ ≠ M ⊆ AM of sets each of M
candidates with the following property: If BM ∈ AM doesn’t satisfy
Droop proportionality, then BM ∉ M.
5
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
3. Free Riding
The fact, that more and more communities, that use STV methods,
change from manual count to computer count, gives us today the possibility
to check hypotheses that have been made in the past about possible voting
behaviours. In this section, we use the ballot data of the 1999, the 2001, the
2003, and the 2005 City Council and School Committee elections in
Cambridge, Massachusetts, to estimate the number of voters who use a
voting behaviour that has been predicted e.g. by Woodall (1983) and
Tideman (2000). The predicted voting behaviour is a so-called free riding
strategy. We describe free riding strategies in general and the free riding
strategy predicted by Woodall and Tideman (section 3.1) and the one
predicted by Hylland (1992) (section 3.2) in particular.
The “single transferable vote resists strategic voting” is the title of a wellknown and frequently quoted paper by Bartholdi (1991). This title also
reflects the opinion of many scientists. For example, Bowler (2000a) writes
about tactical voting under STV:
“To do so, voters would have to know the preference orderings of
every other voter and the number of candidates being run. Even after
they knew this information, voters then could not sit idly by but would
have to begin to calculate the order in which candidates will get
eliminated or elected and would also have to begin to conceive
counterstrategies against all the other voters who would be similarly
calculating what will happen if they altered their preference ordering
over the parties. To put it mildly, this would seem an impossible task.
In fact, STV generally presents such difficult calculations to voters
seeking to behave tactically that it seems to make little sense to do
anything other than register a sincere preference for the party that they
would most like to see win.”
On the other side, there are many scientists who consider STV methods to
be highly manipulable. This discrepancy is caused by the fact that the first
group of scientists considers only strategies that are known from singlewinner elections, while the second group of scientists considers free riding
strategies, i.e. strategies that misuse the fact that in multi-winner elections,
but not in single-winner elections, it is advantageous not to waste one’s vote
by voting for a candidate who would be elected even without one’s vote.
Unfortunately, voters usually understand the usefulness of free riding
strategies very fast so that e.g. it happens less and less frequently that
candidates are elected with full quotas of first preferences. Brams (1996) and
Kleinman (2003) observe a strong incentive of voters to rank more popular
candidates insincerely low and less popular candidates insincerely high.
Warren (1999a) observes that “one can get more out of one’s single vote by
not giving one’s first preference to a handsomely supported candidate.”
Hatton (1920) writes about the elections in 1919 to the 7 seats of the
Kalamazoo City Council:
“The first six candidates in number of first choice votes were
elected and the seventh place went to Albert J. Todd who (with 3.4%)
stood eleventh on the list. As a member of the commission the work of
Todd had been efficient and thoroughly satisfactory. The small
number of first choices which he received was apparently due to the
expectation of a large majority of the voters that his re-election was a
6
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
matter of course. As a result many who desired his re-election marked
their ballots with a first-choice for candidates whom they favored, but
whose success did not seem so well assured, and gave Todd a later
choice. The result was a splendid vindication of the logic and accuracy
of the Hare system.”
Weaver (1995) writes about the 17 elections 1927–1959 to the 7 seats of
the Hamilton City Council:
“As in most electoral systems, strategic voting appears to have
affected outcomes. Over time surpluses of popular candidates seemed
to shrink as their supporters learned to give their first-choice votes to
candidates less assured of election.”
We call the two most important free riding strategies Woodall free riding
and Hylland free riding, since Woodall (1983) and Hylland (1992) were the
first ones who described these free riding strategies explicitly.
3.1. Woodall Free Riding
Woodall free riding is a useful strategy only for those STV methods
where votes of eliminated candidates cannot be transferred to already elected
candidates and therefore jump directly to the next highest ranked hopeful
candidate (leap-frogging). A Woodall free rider is a voter who gives his first
preference to a candidate who is believed by this voter to be eliminated early
in the count even with this voter’s first preference. With this strategy, this
voter assures that he does not waste his vote for a candidate who is elected
already during the transfer of the initial surpluses.
Woodall (1983) writes:
“The biggest anomaly is caused by the decision, always made, not
to transfer votes to candidates who have already reached the quota of
votes necessary for election. This means that the way in which a given
voter’s vote will be assigned may depend on the order in which
candidates are declared elected or eliminated during the counting, and
it can lead to the following form of tactical voting by those who
understand the system. If it is possible to identify a candidate w who is
sure to be eliminated early (say, the Cambridge University Raving
Loony Party candidate), then a voter can increase the effect of his
genuine second choice by putting w first. For example, if two voters
both want a as first choice and b as second, and a happens to be
declared elected on the first count, then the voter who lists his choices
as ‘a v b v ...’ will have (say) one third of his vote transferred to b,
whereas the one who lists his choices as ‘w v a v b v ...’ will have
all of his vote transferred to b, since a will already have been declared
elected by the time w is eliminated. Since one aim of an electoral
system should be to discourage tactical voting, this seems to me to be
a serious drawback.”
Tideman (2000) writes:
“People who understand STV well have developed a strategy for
increasing the influence of their votes, based on this feature of the
Newland-Britton (1997) rules. The strategy is to name as one’s first
choice a candidate who is expected to be one of the first candidates
7
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
excluded. All initial surpluses will have been transferred when this
candidate is excluded, so none of the power of one’s vote is expended
on electing candidates who can be elected without one’s help. Thus
one can have greater influence over the remaining choices. Once, in
the elections for the Board of the Electoral Reform Society, a
candidate ran on the platform that he was the candidate for whom
voters should vote if they did not want their votes wasted on someone
who could be elected without their votes; he was nearly elected.”
However, Woodall free riding can be prevented by restarting the STV
count with the remaining candidates whenever a candidate has been
eliminated. Actually, the Meek (1969, 1970; Hill, 1987) method and the
Warren (1994) method do this. Therefore, Woodall (1983) and Tideman
(1995, 2000) suggest that one of these methods should be used.
A good test for Woodall free riding is an STV election with write-in
options ( i.e. with the possibility for the voters to vote for any person by
writing this person’s name on the ballot ). The City Council and the School
Committee of Cambridge, Massachusetts, are elected by a traditional STV
method that is vulnerable to Woodall free riding and that has write-in
options. In the elections to the 9 seats of the City Council, the voter can vote
for up to 9 write-ins. In the elections to the 6 seats of the School Committee,
the voter can vote for up to 6 write-ins. Here the optimal Woodall free riding
strategy is to give one’s first preference to a completely unimportant write-in.
In table 3.1.1, row “1” contains the numbers of voters in the 1999 City
Council elections (column “CC 1999”), in the 1999 School Committee
elections (“SC 1999”), in the 2001 City Council elections (“CC 2001”), in
the 2001 School Committee elections (“SC 2001”), in the 2003 City Council
elections (“CC 2003”), in the 2003 School Committee elections (“SC
2003”), in the 2005 City Council elections (“CC 2005”), and in the 2005
School Committee elections (“SC 2005”) in Cambridge, Massachusetts.
Row “2” contains the numbers of voters who cast a valid first preference for
a write-in. Row “3” contains the numbers of voters who have to be
subtracted from row “2” because they cast preferences only for write-ins and
who are therefore obviously not Woodall free riders. Furthermore, those
voters who do not cast at least a valid second and a valid third preference
have to be subtracted (row “4”) because these voters cannot be Woodall free
riders. Therefore, row “5” contains the numbers of voters who could be
write-in Woodall free riders.
CC 1999 SC 1999 CC 2001 SC 2001 CC 2003 SC 2003 CC 2005 SC 2005
1
2
3
4
5
18,613
28
9
0
19
17,796
26
5
4
17
17,125
30
12
0
18
16,488
51
32
2
17
20,080
38
16
3
19
18,696
98
66
8
24
16,068
15
9
0
6
Table 3.1.1: Potential write-in Woodall free riders in the 1999, the 2001, the
2003, and the 2005 elections to the City Council and the School Committee
of Cambridge, Massachusetts
In all six elections, the numbers of voters who could be write-in Woodall
free riders are only about 0.1%. In table 3.1.2, N is the number of voters,
T1(b) is the number of voters who cast a valid first preference for candidate
b, T2(b) is the number of voters who cast a valid first preference for
8
15,468
55
36
9
10
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
candidate b and at least also a valid second preference, U is the number of
potential write-in Woodall free riders, and U(b) is the number of potential
write-in Woodall free riders who cast a valid second preference for candidate
b. Table 3.1.2. lists T1(b), T2(b), and U(b) for all those candidates b who are
elected before candidates have to be eliminated. Only in 7 of these 18 cases,
U(b)/U is larger than T2(b)/N. Therefore, also the voters in column “U” seem
to be no Woodall free riders because otherwise super-proportionally many of
these voters would have cast a second preference for a candidate who
reached the quota before candidates had to be eliminated.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
election
CC 1999
SC 1999
CC 2001
CC 2001
CC 2001
SC 2001
SC 2001
SC 2001
CC 2003
SC 2003
SC 2003
SC 2003
SC 2003
SC 2003
SC 2003
CC 2005
SC 2005
SC 2005
candidate b
N
T1(b) T1(b)/N
AD Galluccio
18,613 2,705 14.5%
AL Turkel
17,796 2,617 14.7%
H Davis
17,125 1,713 10.0%
B Murphy
17,125 1,716 10.0%
AD Galluccio
17,125 3,230 18.9%
JG Grassi
16,488 2,135 12.9%
AB Fantini
16,488 2,854 17.3%
AL Turkel
16,488 2,862 17.4%
AD Galluccio
20,080 2,994 14.9%
JG Grassi
18,696 2,295 12.3%
R Harding
18,696 2,362 12.6%
B Lummis
18,696 2,604 13.9%
MC McGovern 18,696 2,716 14.5%
AB Fantini
18,696 2,905 15.5%
N Walser
18,696 3,842 20.5%
AD Galluccio
16,068 2,001 12.5%
AB Fantini
15,468 2,281 14.7%
PM Nolan
15,468 2,387 15.4%
Table 3.1.2: T1(b), T2(b), and U(b) for each candidate b
T2(b) T2(b)/N
2,515 13.5%
2,360 13.3%
1,645 9.6%
1,627 9.5%
2,947 17.2%
1,728 10.5%
2,353 14.3%
2,484 15.1%
2,757 13.7%
1,794 9.6%
1,806 9.7%
2,252 12.0%
2,303 12.3%
2,385 12.8%
3,077 16.5%
1,828 11.4%
1,858 12.0%
2,139 13.8%
who is elected before candidates have to be eliminated
T(a,b) is the number of voters who cast a valid first preference for
candidate a, a valid second preference for candidate b, and at least also a
valid third preference. Woodall free riding is a useful strategy only when one
has at least a sincere first and a sincere second preference. A given voter can
be a Woodall free rider only when he casts at least a valid first, a valid
second, and a valid third preference. When a given voter, whose sincere first
preference is candidate b, uses Woodall free riding, then T2(b) decreases and
for some other candidate a, who is eliminated early in the count, T(a,b)
increases. Therefore, another good test for Woodall free riding is to calculate
T(a,b) for each pair of candidates. If (1) T(a,b)/T1(a) is large compared to
T2(b)/N and (2) T(a,b)/T1(a) decreases with increasing T1(a) for those pairs
of candidates where candidate a is eliminated early in the count and
candidate b is elected before candidates have to be eliminated, then this is an
evidence that voters use Woodall free riding.
Tables 3.1.3 – 3.1.10 contain T(a,b) for each pair of candidates a and b
where candidate b is elected before candidates have to be eliminated. “T1(a)”
contains the numbers of voters who cast a valid first preference for the
candidate in column “candidate a”. The column “Galluccio” (resp. “Turkel”,
resp. “Davis”, etc.) contains the numbers of voters of column “T1(a)” who
9
U U(b) U(b)/U
19
2
10.5%
17
2
11.8%
18
2
11.1%
18
1
5.6%
18
5
27.8%
17
0
0.0%
17
1
5.9%
17
4
23.5%
19
1
5.3%
24
0
0.0%
24
5
20.8%
24
6
25.0%
24
2
8.3%
24
1
4.2%
24
7
29.2%
6
0
0.0%
10
1
10.0%
10
4
40.0%
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
cast a valid second preference for Galluccio (resp. Turkel, resp. Davis, etc.)
and at least also a valid third preference.
In tables 3.1.3 – 3.1.10, T(a,b)/T1(a) rather increases than decreases with
increasing T1(a). Also the prediction, that T(a,b)/T1(a) is large compared to
T2(b)/N, is not fulfilled. This is surprising because, in so far as Woodall free
riding certainly is a useful strategy, one would expect that at least some
voters use this strategy. A possible explanation, why voters do not use
Woodall free riding, is that they fear that, when too many voters give their
first preference to candidate a because they believe that he is eliminated
early in the count, then it could happen that candidate a gets so many votes
that he is elected (Fennell, 1994; Hill, 1994; Tideman, 2000). But this can
only explain why T(a,b)/T1(a) does not decrease so fast with increasing
T1(a); this cannot explain why T(a,b)/T1(a) increases with increasing T1(a).
A possible explanation, why T(a,b)/T1(a) increases with increasing T1(a), is
that voters are confronted with two problems:
1. It is a useful strategy not to waste one’s vote by voting for a
candidate b who is elected even without one’s vote. However, when
too many voters use Woodall free riding and cast a first preference
for candidate a, because they believe that he is eliminated early in
the count even with one’s vote, then it could happen that candidate a
gets so many votes that he is elected.
2. It is a useful strategy not to vote for a candidate a who is believed to
be eliminated with a high probability even with one’s vote, because
otherwise there is the danger that there are no acceptable candidates
anymore to whom this voter could transfer his vote when candidate a
is eliminated. When a voter votes for a candidate a, who is
eliminated with a high probability even with this voter’s vote, and
not for candidate b, who is less preferred but who has great chances
of being elected when he is not eliminated early, then there is the
great danger that candidate b is eliminated before candidate a is
eliminated, so that this voter cannot transfer his vote to candidate b
anymore when candidate a is eliminated.
Because of problem 2, only those voters, who cannot identify themselves
with any of the stronger candidates, vote for candidates who are believed to
be eliminated with a high probability; therefore, T(a,b)/T1(a) is low for low
T1(a) for those candidates b who are elected before candidates have to be
eliminated; therefore, T(a,b)/T1(a) rather increases than decreases with
increasing T1(a).
10
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
candidate a
CO Christenson
DP Wormwood-Malone
WC Jones
AK Nidle
VL Dixon
JJ Chase
DM Giacobbe
JM Williamson
R Winters
H Peixoto
D Hoicka
EC Snowberg
D Trumbull
R Goodwin
DP Maher
K Triantafillou
MA Sullivan
KE Reeves
H Davis
J Braude
TJ Toomey
MC Decker
KL Born
T1(a)
28
28
31
40
44
102
109
128
301
308
325
425
533
805
1,030
1,167
1,321
1,420
1,458
1,480
1,497
1,642
1,658
Galluccio
2 (7.1%)
0 (0.0%)
2 (6.5%)
0 (0.0%)
3 (6.8%)
10 (9.8%)
22 (20.2%)
2 (1.6%)
27 (9.0%)
46 (14.9%)
7 (2.2%)
12 (2.8%)
129 (24.2%)
296 (36.8%)
309 (30.0%)
42 (3.6%)
278 (21.0%)
149 (10.5%)
70 (4.8%)
50 (3.4%)
233 (15.6%)
43 (2.6%)
100 (6.0%)
Table 3.1.3: Potential Woodall free riders in the 1999
City Council elections in Cambridge, Massachusetts
candidate a
SM Burke
JF Patterson
AE Thompson
ML Brazo
D Harding
ET Kenney
M Harshbarger
N Walser
SM Segat
JG Grassi
AB Fantini
D Simmons
T1(a)
212
278
373
471
698
738
1,550
1,894
1,985
2,269
2,277
2,408
Turkel
6 (2.8%)
9 (3.2%)
35 (9.4%)
82 (17.4%)
24 (3.4%)
134 (18.2%)
109 (7.0%)
520 (27.5%)
480 (24.2%)
97 (4.3%)
55 (2.4%)
506 (21.0%)
Table 3.1.4: Potential Woodall free riders in the 1999 School
Committee elections in Cambridge, Massachusetts
11
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
candidate a
JM Williamson
JE Condit
H Peixoto
VL Dixon
RL Hall
J Horowitz
SE Jens
S Iskovitz
EA King
DP Maher
J Pitkin
KE Reeves
MA Sullivan
D Simmons
TJ Toomey
MC Decker
H Davis
B Murphy
AD Galluccio
T1(a)
58
63
69
92
153
155
278
345
378
1,017
1,091
1,141
1,315
1,339
1,402
1,540
1,713
1,716
3,230
Davis
2 (3.4%)
6 (9.5%)
5 (7.2%)
2 (2.2%)
3 (2.0%)
14 (9.0%)
8 (2.9%)
29 (8.4%)
43 (11.4%)
32 (3.1%)
222 (20.3%)
72 (6.3%)
45 (3.4%)
186 (13.9%)
44 (3.1%)
298 (19.4%)
--343 (20.0%)
137 (4.2%)
Murphy
2 (3.4%)
0 (0.0%)
3 (4.3%)
3 (3.3%)
13 (8.5%)
12 (7.7%)
5 (1.8%)
30 (8.7%)
46 (12.2%)
41 (4.0%)
202 (18.5%)
34 (3.0%)
28 (2.1%)
137 (10.2%)
11 (0.8%)
215 (14.0%)
254 (14.8%)
--90 (2.8%)
Galluccio
3 (5.2%)
5 (7.9%)
7 (10.1%)
7 (7.6%)
18 (11.8%)
6 (3.9%)
35 (12.6%)
9 (2.6%)
25 (6.6%)
304 (29.9%)
48 (4.4%)
125 (11.0%)
316 (24.0%)
74 (5.5%)
272 (19.4%)
163 (10.6%)
114 (6.7%)
105 (6.1%)
---
sum
7 (12.1%)
11 (17.5%)
15 (21.7%)
12 (13.0%)
34 (22.2%)
32 (20.6%)
48 (17.3%)
68 (19.7%)
114 (30.2%)
377 (37.1%)
472 (43.3%)
231 (20.2%)
389 (29.6%)
397 (29.6%)
327 (23.3%)
676 (43.9%)
Table 3.1.5: Potential Woodall free riders in the 2001
City Council elections in Cambridge, Massachusetts
candidate a
VJ Delaney
F Baker
ML Erlien
SM Segat
N Walser
R Harding
AC Price
JG Grassi
AB Fantini
AL Turkel
T1(a)
Grassi
240
23 (9.6%)
324
28 (8.6%)
1,193 21 (1.8%)
1,590 61 (3.8%)
1,677 42 (2.5%)
1,689 172 (10.2%)
1,873 41 (2.2%)
2,135
--2,854 942 (33.0%)
2,862 97 (3.4%)
Fantini
29 (12.1%)
62 (19.1%)
25 (2.1%)
107 (6.7%)
68 (4.1%)
156 (9.2%)
71 (3.8%)
698 (32.7%)
--133 (4.6%)
Turkel
5 (2.1%)
9 (2.8%)
272 (22.8%)
619 (38.9%)
596 (35.5%)
176 (10.4%)
319 (17.0%)
94 (4.4%)
158 (5.5%)
---
Table 3.1.6: Potential Woodall free riders in the 2001 School
Committee elections in Cambridge, Massachusetts
12
sum
57 (23.8%)
99 (30.6%)
318 (26.7%)
787 (49.5%)
706 (42.1%)
504 (29.8%)
431 (23.0%)
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
candidate a
DJ Greenwood
VL Dixon
RL Hall
RJ LaTrémouille
L Taymorberry
EA King
AL Smith
CK Bellew
CA Kelley
J Pitkin
D Simmons
DP Maher
MS DeBergalis
B Murphy
MC Decker
KE Reeves
TJ Toomey
MA Sullivan
H Davis
T1(a)
39
64
96
126
188
361
480
735
992
1,010
1,181
1,190
1,206
1,362
1,378
1,525
1,613
1,656
1,846
Galluccio
1 (2.6%)
9 (14.1%)
11 (11.5%)
3 (2.4%)
2 (1.1%)
46 (12.7%)
5 (1.0%)
61 (8.3%)
98 (9.9%)
49 (4.9%)
38 (3.2%)
340 (28.6%)
54 (4.5%)
72 (5.3%)
146 (10.6%)
127 (8.3%)
330 (20.5%)
404 (24.4%)
136 (7.4%)
Table 3.1.7: Potential Woodall free riders in the 2003
City Council elections in Cambridge, Massachusetts
candidate a
T1(a)
C Craig
573
AC Price
1,301
JG Grassi
2,295
R Harding
2,362
B Lummis
2,604
MC McGovern 2,716
AB Fantini
2,905
N Walser
3,842
Grassi
25
(4.4%)
27
(2.1%)
--285
(12.1%)
71
(2.7%)
111
(4.1%)
933
(32.1%)
179
(4.7%)
Harding
20
(3.5%)
180
(13.8%)
229
(10.0%)
--217
(8.3%)
238
(8.8%)
176
(6.1%)
509
(13.2%)
Lummis McGovern Fantini
169
89
59
(29.5%) (15.5%) (10.3%)
241
147
64
(18.5%) (11.3%) (4.9%)
43
77
651
(1.9%)
(3.4%) (28.4%)
182
161
192
(7.7%)
(6.8%)
(8.1%)
637
96
--(24.5%) (3.7%)
614
191
--(22.6%)
(7.0%)
102
155
--(3.5%)
(5.3%)
468
318
253
(12.2%) (8.3%)
(6.6%)
Table 3.1.8: Potential Woodall free riders in the 2003 School
Committee elections in Cambridge, Massachusetts
13
Walser
47
(8.2%)
360
(27.7%)
146
(6.4%)
244
(10.3%)
356
(13.7%)
355
(13.1%)
165
(5.7%)
---
sum
409
(71.4%)
1,019
(78.3%)
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
candidate a
JE Condit
RL Hall
RJ LaTrémouille
AL Green
B Hees
LJ Adkins
JA Gordon
DP Maher
S Seidel
CA Kelley
KE Reeves
B Murphy
D Simmons
TJ Toomey
H Davis
MA Sullivan
MC Decker
T1(a)
42
75
118
181
198
243
626
902
973
1,042
1,207
1,236
1,330
1,432
1,459
1,464
1,524
Galluccio
1 (2.4%)
6 (8.0%)
2 (1.7%)
10 (5.5%)
12 (6.1%)
11 (4.5%)
31 (5.0%)
204 (22.6%)
46 (4.7%)
72 (6.9%)
110 (9.1%)
50 (4.0%)
62 (4.7%)
260 (18.2%)
68 (4.7%)
318 (21.7%)
163 (10.7%)
Table 3.1.9: Potential Woodall free riders in the 2005
City Council elections in Cambridge, Massachusetts
candidate a
MC McGovern
B Lummis
L Schuster
R Harding
JG Grassi
N Walser
AB Fantini
PM Nolan
T1(a)
1,413
1,514
1,843
1,981
1,990
2,004
2,281
2,387
Fantini
82 (5.8%)
77 (5.1%)
63 (3.4%)
165 (8.3%)
559 (28.1%)
191 (9.5%)
--86 (3.6%)
Nolan
230 (16.3%)
170 (11.2%)
362 (19.6%)
115 (5.8%)
58 (2.9%)
324 (16.2%)
87 (3.8%)
---
sum
312 (22.1%)
247 (16.3%)
425 (23.1%)
280 (14.1%)
617 (31.0%)
515 (25.7%)
Table 3.1.10: Potential Woodall free riders in the 2005 School
Committee elections in Cambridge, Massachusetts
14
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
3.2. Hylland Free Riding
Problem 1 can be circumvented by using Hylland free riding instead of
Woodall free riding. Unlike Woodall free riding, Hylland free riding can be
used under any STV method. Hylland writes (1992):
“Both for groups and for individual voters it could be advantageous
not to vote for a candidate who is considered certain of winning
election, even if that candidate is one’s first choice. Suppose that my
true first and second choices are a and b, I am sure a will get many
more first preferences than needed for election, but I find b’s chances
uncertain. If I list a as the first preference on my ballot, its weight is
reduced before it reaches b. If I omit a, b gets a vote with full weight.”
In short, a Hylland free rider is a voter who omits in his individual
ranking completely all those candidates who are certain to be elected. Of
course, when too many voters use Hylland free riding then it can happen that
the candidate with the cast first preference is elected while the candidate
with the sincere first preference is eliminated. However, when a voter uses
Hylland free riding then the candidate with the cast first preference is one of
this voter’s favorite candidates, while when this voter uses Woodall free
riding then the candidate with the cast first preference is a candidate who this
voter does not want to be elected. Therefore, although both free riding
strategies can backfire, such a backfire is less severe under Hylland free
riding than under Woodall free riding.
Problem 2 can be circumvented by voting only for those candidates who
are believed to be in the race until the final count. In so far as a candidate will
be in the final count when he has more than N/(M+2) first preferences, it is a
useful strategy to cast one’s first preference only for one of those candidates
who are believed to get between N/(M+2) and N/(M+1) first preferences.
This voting behaviour could best be observed in Canada, because here the
city councils were elected by a traditional STV method for a one year term
and in a single city-wide district so that the voters had very precise
information about the support of the different candidates. A consequence of
this voting behaviour was that usually almost all first preferences were
concentrated on M+1 almost equally strong candidates (Berger, 2004; Harris,
1930; Johnston, 2000; Pilon, 1994), so that the weakest of these M+1
candidates was eliminated and the winners happened to be those M
candidates with the largest numbers of first preferences. Johnston (2000)
writes that one of the main criticisms of STV was that it was “one of the
most common features of PR in Canadian municipal elections” that “the
final count closely mirrored the results of the first count”. Pilon (1994)
writes that the main problem of STV in Canada was that it “did not seem to
make much difference in the results. After days of counting, eliminating
candidates, and transferring fractions of support from one aspirant to
another, there was little difference between the first choice results and the
final tally.” And Berger (2004) writes: “Complexity and the discovery that
STV elected in most cases the same persons as would have been elected had
only first preferences been counted, were the two most frequently given
explanations for public indifference and support for repeal.”
The same voting behaviour was also observed in the Isle of Man. The
lower house (House of Keys) was elected by a traditional STV method. Also
here the winners always happened to be those candidates with the largest
numbers of first preferences. This led to the abolition of STV in 1995
(Herbert, 2003).
15
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
3.3. Summary
A free rider is a voter who misuses the fact that, in multi-winner
elections, it is a useful strategy not to vote for a candidate who will be
elected even without one’s vote. Free riding is a very serious problem of
STV methods. The two free riding strategies that have been predicted in the
literature are Woodall (1983) free riding and Hylland (1992) free riding.
A Woodall free rider is a voter who gives his first preference to a
candidate who is believed by this voter to be eliminated early in the count
even with this voter’s first preference; with this strategy, this voter assures
that he does not waste his vote for a candidate who is elected already during
the transfer of the initial surpluses. A Hylland free rider is a voter who omits
in his individual ranking completely all those candidates who are certain to
be elected.
It is not possible to extract the number of Hylland free riders simply from
the ballot data. But with additional assumptions, it is possible to extract the
number of Woodall free riders. We used the ballot data of the 1999, the
2001, the 2003, and the 2005 City Council and School Committee elections
in Cambridge, Massachusetts, to estimate the number of voters who use
Woodall free riding. We could not find any evidence at all that voters use
this strategy. Possible explanations, why voters do not use this strategy, are:
(a) When too many voters cast a first preference for candidate a, not
because he is their sincere first preference but because they believe
that he will be eliminated early in the count, it could happen that this
candidate gets so many votes that he is elected (Fennell, 1994; Hill,
1994; Tideman, 2000).
(b) It is not useful to vote for a candidate a who is eliminated with a
high probability, because it could happen that there are no acceptable
candidates anymore to whom this voter could transfer his vote when
candidate a is eliminated.
(c) When a voter considers his second favorite candidate to be only
slightly worse than his favorite candidate, then Hylland (1992) free
riding is less dangerous than Woodall (1983) free riding, in so far as
a backfire is less severe under Hylland free riding than under
Woodall free riding.
(d) The political organizations have not yet found a simple way to use
Woodall free riding on a larger scale to increase their numbers of
seats. Therefore, the voters are usually not pointed to this strategic
problem.
On the other side, we quoted several empirical papers on STV that
demonstrate that Hylland free riding is a frequently used strategy (Berger,
2004; Harris, 1930; Johnston, 2000; Pilon, 1994).
16
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
4. Vote Management
Vote management is a practice that seems to have acquired the
same degree of mystique as alchemy, a technique that, in some
eyes, can be used to conjure a seat out of even the most meagre
bundle of first preferences.
Michael Gallagher (1993a)
In multi-winner elections, the term vote management (or vote allocation)
refers to strategies where a party divides the electorate into parts and asks all
the voters of the same part to vote in the same manner (prescribed by this
party in advance and for each part in a different manner). Usually, these
parts are also known as pockets or bailiwicks and this strategy is also known
as bailiwicking only when the electorate is divided according to geographic
or social criteria; but for the sake of simplicity, we will use these terms also
when the electorate is divided according to other criteria. Under STV
methods, this strategy is also known as spread the preferences (STP)
(Farrell, 1993, 2000).
Vote management is also used e.g. under the single non-transferable vote
(SNTV) (Cox, 1997; Grofman, 1999; Lijphart, 1986), under limited voting
(Hoag, 1926; Lijphart, 1986), and under cumulative voting (Bowler, 2003).
However, the aim of this paper is to give an overview over vote management
strategies mainly under STV methods (Barber, 1995; Bax, 1973; Bowler,
1991a, 1991b, 2000b; Busteed, 1990; Farrell, 1992, 1996, 2000; Gallagher,
1990b, 1992, 1993b, 2003b; Laver, 1987, 1998; Mair, 1987a, 1987b; Parker,
1982; Penniman, 1987; Sacks, 1970, 1976).
In section 4.1, typical examples for vote management strategies are
presented. In sections 4.2 – 4.6, those 5 questions, that have to be answered
by that party that wants to run a vote management strategy successfully, are
discussed.
4.1. Some Examples
A typical example looks as follows (Busteed, 1990; Mair, 1987a, 1987b)
(Taoiseach = Prime Minister; Tánaiste = Deputy Prime Minister; Seanad =
upper house; Dáil = lower house; TD = Teachta Dála = member of the Dáil):
“1921–1982 the Corish family had held a seat for Labour in the
Wexford constituency, but on the retirement of the Labour TD
Brendan Corish (Labour leader 1960–1977 and Tánaiste 1973–1977)
in February 1982 his brother Desmond Corish had failed to hold the
seat, and it had gone to Fianna Fáil so that this 5-seat constituency
(65,000 registered voters) had resulted in three seats for Fianna Fáil
and two seats for Fine Gael. Suspecting that one of the Fianna Fáil
seats was vulnerable, Fine Gael proceeded on two fronts. It first
decided to breach a long-standing local agreement that it would never
seriously challenge a Labour candidate based on the Corish family
home base of Wexford Town. Because both Fine Gael TDs came from
the north and centre of this constituency, the Constituency Review
Committee recommended that a third candidate be nominated from
the southern end, the area that included the towns of Wexford (where
18,000 voters were registered) and New Ross (where 8,000 voters
were registered). With a reasonably strong potential candidate from
this area, Avril Doyle, the first lady mayor of Wexford Town and
17
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
from a family long involved in Fine Gael, the party believed that her
nomination and a more judicious division of first preferences between
the two incumbents could give the party a third seat. The strategy
worked perfectly. Although Fine Gael’s overall vote share rose, the
number of first preferences won by its two incumbent TDs Michael
Joseph d’Arcy and Ivan Yates fell slightly, as intended (Fine Gael:
Feb. 1982 37.7% [3.3% to the unsuccessful candidate Louise
Hennessy], Nov. 1982 41.4%; d’Arcy: Feb. 1982 18.0%, Nov. 1982
15.8%; Yates: Feb. 1982 16.4%, Nov. 1982 14.2%). Both had
sufficient votes to ensure their own election, but the reduction in their
total gave Doyle (11.4%) sufficient first preferences to remain ahead
of the Labour candidate (Brendan Howlin: 9.9%). Because Labour’s
transfers were likely to go predominantly to Fine Gael (as would Fine
Gael’s go to Labour in similar circumstances), Doyle’s consistent
plurality over the Labour candidate meant that she would benefit from
his earlier elimination. This followed the fourth count, when Doyle
had accumulated 6,140 (12.2%) against 5,481 (10.9%) votes for the
Labour candidate. After his elimination, 4,364 lower-preference votes
passed to Fine Gael, a transfer sufficient to push the two incumbents
past the quota while at the same time placing Doyle close enough to
be assured of election.”
Gallagher (1999) describes the vote management strategies during the
Dáil elections in 1997:
“Both major parties sought to manage the vote in specific
constituencies. For example, in the five-seater Dun Laoghaire, a
Fianna Fáil target seat, the long-serving TD David Andrews had often
taken too high a percentage of the Fianna Fáil vote (72.5% in 1992),
and his running mate had trailed too far behind to be elected.
Consequently, with Andrews’ agreement, the local organisation
divided the constituency into two, and voters were sent or handed
items of campaign literature asking them to vote in particular ways.
One, headed ‘Fianna Fáil Vote Management Strategy’, showed a map
of the constituency divided into two areas so that all voters would
know which candidate to give their first preference to in order to
maximise the party’s chances of winning two seats. In the event, the
balance between the two candidates was more even than at previous
elections, and Fianna Fáil gained a second seat.
Meanwhile, Galway East had changed from a three-seater to a
four-seater, and Fianna Fáil, Fine Gael, and the Progressive
Democrats all had a good chance of taking the additional seat. Fine
Gael devised what was termed the ‘railway line strategy’, based on the
Dublin-Galway line that ran from east to west across the middle of the
constituency. Voters living north of the line were asked to give their
first preference to Paul Connaughton and their second to Ulick Burke;
those living to the south were asked to switch those preferences. This
plan required some sacrifice on the part of Connaughton, the
incumbent TD, who had built up a degree of personal support south of
the line by his constituency work and who in a free and open contest
would have been certain of re-election. The strategy worked well and
was crucial in Fine Gael’s capture of the additional seat.”
18
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Gallagher (2003a) describes the vote management strategies during the
Dáil elections in 2002:
“There were a number of examples of vote management schemes
in 2002. Sometimes parties explicitly called on their voters to vote a
certain way. For example, in Wexford, where Fianna Fáil was making
a determined effort to take three seats, the party produced a newspaper
advertisement showing a map of the constituency, with different areas
shaded in different colours. Those living in the areas coloured yellow,
basically the central belt, were asked to give a first preference to John
Browne; those living in a purple area (the north-east and the southeast) were asked to vote for Tony Dempsey, and those in a greencoloured area (the south-west and north-west) were asked to vote first
for Hugh Byrne. In the event the vote was reasonably well balanced
but the effort was in vain as the party simply didn’t receive enough
votes, and it was the independent Liam Twomey who took the seat
that Fine Gael lost.
In the same constituency, vote management within the Fine Gael
camp ran less smoothly. Avril Doyle, a former TD and now an MEP,
had been persuaded to return to fight the election sine Fine Gael was
in great danger of losing a seat given that its long-standing incumbent
Ivan Yates was retiring. However, the other candidates were not keen
to allow her as much territory as she wanted. She appealed to the
party’s national headquarters, and it duly barred Paul Kehoe (Yates’
successor) from canvassing in an area north-east of Wexford town.
Doyle explained, ‘I insisted that I have the Wexford district’, pointing
out that she lived there. Kehoe, who had previously been canvassing
there, was not pleased, but said he would abide by the decision, and
there was some surprise and resentment that Doyle had appealed to
the national body rather than having the dispute resolved within the
constituency organisation. In the event Kehoe was elected and Doyle
finished last of the three Fine Gael candidates.
The five-seat Mayo constituency saw plenty of turf wars —
sometimes reminiscent of great power disputes during the nineteenth
century — within both major parties. Fights broke out between
supporters of rival Fianna Fáil candidates Beverley Cooper-Flynn and
Tom Moffatt over who had the right to hold a collection outside a
church gate in Foxford. Cooper-Flynn explained that the four Fianna
Fáil candidates had signed up to an agreement about who had the right
to which territory, but within two hours ‘people were breaking it all
over the place’; she herself was still respecting it, she said, ‘for the
moment anyway’. Things were no better within Fine Gael. The vote
management scheme there entailed damping down the vote of the
frontrunner, Michael Ring, and boosting support for the two other
incumbents, Jim Higgins and Enda Kenny, who were seen as more
vulnerable. The Fine Gael constituency organisation thus decided that
Ring would be ‘kept out of’ certain areas in south Mayo, even though
he had been holding monthly clinics there over the previous five
years. Ring was said to be further displeased when he was asked to
relinquish some ground on the east side of Erris to the party’s fourth
candidate Ernie Caffrey, in exchange for some presumably less
promising territory around Foxford.”
19
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Gallagher (2008a) describes the vote management strategies during the
Dáil elections in 2007:
“Characteristically, vote management entails dividing the
constituency geographically and, like handing out slices of a pie,
awarding sections of it to individual candidates. In urban areas, an
alternative approach that keeps candidates apart without formally
dividing the territory involves allowing each candidate to canvass the
whole constituency but making sure that only one candidate is in a
particular area at a time. Candidates may be told which areas they are
and are not permitted to canvass, and voters may be asked to vote in a
particular way depending on which part of the constituency they live
in. For example, in the Wexford constituency Fianna Fáil awarded
each of its three candidates sole canvassing rights in their home area,
while the Gorey area was divided among them down to the level of
individual polling boxes. Within Fine Gael, the New Ross electoral
area was open territory, and, moreover, each candidate was allowed to
canvass one day a week in the other candidates’ areas provided this
was arranged in advance. Candidates will, of course, expect to be
given the area around their home base, and so the borders of their
respective bailiwicks, like a disputed frontier between states, are
where trouble is most likely to flare. Matters can become particularly
tense if one candidate is perceived as a front-runner, in which case
vote management requires trying to siphon some of his or her support
to the weaker member of the team. As well as provoking resistance
from the front-runner, this tactic, if pushed too far, might have the
unintended effect of leading to the election of the weaker candidate at
the expense of the front-runner, thus costing the party one of its
leading lights, as happened in Cork North-West in 2002 when a Fine
Gael vote management plan backfired and the front-bencher Michael
Creed lost his seat as a result.
When party support seems to be slipping candidates become edgy
and the normal courtesies of intra-party conduct may be cast to the
winds. In Cork East the two Fianna Fáil incumbents took their gloves
off in the run-up to polling day. Michael Ahern, based in the south of
the constituency, appealed for support from the northern area, the
bailiwick of Ned O’Keeffe. Traditional boundaries, he said, meant
nothing in this election: ‘At the last election there was a boundary in
place which he [O’Keeffe] broke lock, stock and barrel right up to my
doorstep. This time there is no boundary so it is open territory.’
O’Keeffe, who had had to resign a junior ministerial position in 2001
and had then suffered the further pain of seeing Ahern appointed to
the equivalent position in June 2002, said that if Ahern had performed
competently in his ministerial post Fianna Fáil would have been
pressing for three seats in the constituency instead of having to worry
about holding on to two. Ahern rounded off the exchange by opining
that some of O’Keeffe’s comments amounted to slander, though he
did not intend to take legal action. In the event, as at every election
since November 1982, both Ahern and O’Keeffe were comfortably reelected.
In Dublin Central vote management takes on a different meaning
altogether. Fianna Fáil usually wins around 40% of the votes here,
making it competitive for two seats. Whereas the logic outlined above
would suggest something like an even division of the votes between
two candidates, the local constituency organisation, dominated by
party leader Bertie Ahern, operates instead the tactic of trying to
20
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
maximise Ahern’s first preference support in the hope that enough
votes will transfer from his surplus on to his running mate(s) to secure
a second seat. Neutral observers believe that when Fianna Fáil has
taken two seats in Dublin Central it has been despite rather than
because of this singular approach, but, undaunted, the organisation
repeated the tactic in 2007. Ahern received 12,734 first preferences,
83% of the party total. On this occasion he had two running mates —
reportedly this was simply because he had been unable to decide
which one to drop from the ticket, and so let them both stand — and
they were in effect competing for Ahern’s second preferences, with
the winner likely to take a seat. Although Mary Fitzpatrick received
more first preferences than Cyprian Brady (1,725 compared with 939),
Brady, a long-time member of Ahern’s constituency organisation,
received over 1,000 more of Ahern’s second preferences than she did
and went on to take the seat. It turned out that the party organization
had distributed 30,000 leaflets early in the morning of election day
asking voters to vote 1-2-3 in that order for Ahern, Brady and
Fitzpatrick. While, Fitzpatrick said, ‘I never thought they were the
Legion of Mary’, she had not expected the party to ‘shaft’ and
‘undermine’ her as it had. However, one of Ahern’s associates in the
constituency, Chris Wall, explained that Fitzpatrick had brought her
fate upon herself by firing the first shot: she had distributed campaign
literature in some areas asking voters to give her their first preference.
Wall said: ‘She was asked not to do this sort of thing. Having then
done it, she therefore effectively set in train a motion she wasn’t going
to be able to stop.’”
Vote management is neither an invention of the 1970s or 1980s nor a
pure Irish phenomenon. This strategy can be observed everywhere where
STV is being used. In the history of vote management under STV, that
example that attracted most attention was the vote management strategy of
the Republican Party during the elections to the Cincinnati City Council in
1925. The Cincinnati City Council was elected by STV in a single 9-seat
constituency. The Republican Party hoped to win 6 of the 9 seats. Therefore,
it divided Cincinnati into 6 bailiwicks and nominated 6 candidates a, b, c, d,
e, and f. It asked its supporters to vote a v b v ... in the first bailiwick, b v
a v ... in the second bailiwick, c v d v ... in the third bailiwick, d v c v ...
in the fourth bailiwick, e v f v ... in the fifth bailiwick, and f v e v ... in
the sixth bailiwick. However, the strategy of the Republican Party failed
mainly because it overestimated its support. Goldman (1930) writes:
“The regular Republican organization has been experimenting, but
has apparently not yet found a way to ‘beat the system.’ In the first
election it thought that it would gain strength by concentrating on only
six candidates. But it found that this was a source of weakness,
because it had fewer candidates than it might have had to rally its
friends to the tickets and so pass on additional votes to its leading
candidates when they were eliminated. It also attempted to district the
city by wards, by dictating to its voters in each ward, not only for what
group of candidates they should vote, but in what order they should
vote them. In this it failed signally in several wards, because the voters
would not accept the dictated first-choice candidate. It also tried to
pair candidates, with the result that only one of each pair was elected,
and not the strongest candidate.”
21
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Harris (1930) writes:
“The Republican organization was obviously puzzled to know
what tactics to adopt to win the election. Not understanding the
fundamentals of PR, it decided to put only six candidates in the field,
and to assign each to a particular district. It was believed that this
arrangement would permit the organization to beat the system. The
candidates were also assigned in pairs, each candidate being instructed
to solicit second-choice votes for the candidate with whom he was
paired. As the campaign progressed, this led to a great deal of friction.
Dissension broke out within the ranks, for certain candidates thought
they were being double crossed, and others believed that they were
assigned to difficult districts. Then, too, many voters resented being
told in what order to vote, and this lost votes. The assignment was
unhappy in several instances. For example, Adolph Kummer,
President of the Central Labor Union, was assigned to a district which
contained some of the wealthiest residential sections of the city. The
favored organization candidates were assigned to the Republican
strongholds.”
Kolesar (1995) writes:
“The Republican organization waged an inept campaign. Rather
than nominate a full slate, they chose only six candidates. They
‘districted’ the city among the six, but, ‘as the fight got hotter and the
Republican nominees saw that the machine could not assure the
victory of all six candidates, they commenced to fight among
themselves. Friends of Republican candidates sought first choice votes
in districts that had been apportioned to other Republican candidates’
(Bentley, 1926; Taft, 1933). The Charter Committee elected six of its
nominees to the council; the Republican organization, only three.”
Over a very long time, the unsuccessful vote management strategy of the
Republican Party during the Cincinnati City Council elections in 1925 was
used as an evidence that vote management does not work in the USA.
However, Shaw (1954) describes the vote management strategy of the
Democratic Party during the New York City Council elections in 1937–1945
as follows:
“After watching their candidates compete against each other in
borough-wide elections in 1937, they evolved their own technique for
obtaining maximum representation. Each borough was divided into
the same number of zones as the number of councilmen it seemed
likely to select. Within each zone the district leaders agreed upon a
candidate. Then the entire slate was reviewed by the County Leader
and Executive Committee, who ordered the party’s adherents to
follow an identical pattern of voting — i.e. the number to be placed
beside each candidate’s name in each zone was determined in
advance. Proportionalists and their opponents agree that under this
system in the 1939 election the Democrats massed their strength for
optimum effectiveness.”
With this strategy, the Democratic Party usually won about two thirds of
the seats of the New York City Council with about half of the first
preferences (Hallett, 1941, 1946; Hermens, 1968; McCaffrey, 1939; Shaw,
1954; Zeller, 1947).
22
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
4.2. Equalizing of First Preferences and Later Preferences
A party that wants to run a vote management strategy successfully is
confronted with five problems. The first problem is: How should the voters
in the different bailiwicks vote?
Equalizing the First Preferences: Suppose that the party tries to win 6
seats. Then this party will divide the electorate into 6 bailiwicks and
nominate 6 candidates a, b, c, d, e, and f. When it is sufficient to equalize the
numbers of first preferences, then the party will simply ask all its supporters
in the first bailiwick to give their first preferences to candidate a, all its
supporters in the second bailiwick to give their first preferences to candidate
b, all its supporters in the third bailiwick to give their first preferences to
candidate c, etc..
Equalizing the Permutations: When also the numbers of the lower
preferences have to be equalized, then the optimal strategy would be to
divide the electorate into as many bailiwicks as there are permutations of
candidates (here: 6! = 720) and to allocate to each bailiwick one of these
permutations and to ask all the supporters of this bailiwick to rank the
candidates according to this permutation. However, such a strategy would be
impracticable; and simply asking the supporters to rank the candidates in a
random manner would rather make the voters rank the candidates in that
permutation in which the candidates are listed on the ballot than lead to an
even distribution of the possible permutations. A practicable simplification
of this strategy is to divide the electorate into 6 bailiwicks and to ask all the
supporters in the first bailiwick to vote a v b v c v d v e v f, all the
supporters in the second bailiwick to vote b v c v d v e v f v a, all the
supporters in the third bailiwick to vote c v d v e v f v a v b, etc..
Grouping: Another practicable simplification is to group the candidates
and to divide the electorate into as many bailiwicks as there are groups of
candidates. Then each bailiwick is divided into as many sub-bailiwicks as
there are permutations of the candidates of this group. For example, when
the candidates are divided into two groups abc and def then each bailiwick is
divided into 3! = 6 sub-bailiwicks; in these 12 sub-bailiwicks the voters are
asked to vote a v b v c v ..., a v c v b v ..., b v a v c v ..., b v c v a
v ..., c v a v b v ..., c v b v a v ..., d v e v f v ..., d v f v e v ..., e
v d v f v ..., e v f v d v ..., f v d v e v ... resp. f v e v d v .... The
vote management strategy of the Republican Party during the Cincinnati
City Council elections in 1925 is an example of such a grouping strategy.
The equalization of the permutations becomes the more important and
simultaneously the more impracticable the larger the number of seats per
constituency gets. Therefore, in Ireland, where the electorate is usually
divided into 3- to 5-seat constituencies, a party usually only tries to equalize
the numbers of first preferences of its candidates, while in the USA, where
the electorate is usually divided into 7- to 9-seat constituencies, a party has
to find a compromise in this trade-off. Grouping the candidates can be such a
compromise.
4.3. Number of Candidates
The second problem is: How many candidates should be nominated?
Suppose C0 is the number of candidates nominated by that party that runs
a vote management strategy. C0 must not be chosen too large (compared to
the number of seats this party could realistically win) because otherwise the
candidates are too far below the Droop quota N/(M+1) and eliminated early
23
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
(Cohan, 1975, 1978; Lijphart, 1979). When C0 is chosen too large then there
is also the danger that the candidates do not participate at the vote
management strategy, since the probability that they will belong to the
elected candidates is low; these candidates will rather spend most of their
time and money to fight against candidates of their own party (Bax, 1973;
Bowler, 1991b; Mair, 1987a; Yates, 1990).
On the other side, when C0 is chosen too pessimistically then it can
happen (a) that the party wastes seats by nominating fewer candidates than it
could have won seats, (b) that politicians who have not been nominated, but
who believe that the party could possibly win more seats than it has
nominated candidates, run as independent candidates (Busteed, 1990;
Holmes, 1999) or (c) that the party is punished by the voters of a certain
minority for not having nominated politicians of this minority (Gallagher,
1980; Mair, 1987a). A large number of candidates also leads to a higher
turnout among the supporters of this party; the larger the number of
candidates is the larger is the number of supporters who feel represented by
at least one candidate and who, therefore, go to the polls and cast a vote that
will — as soon as their favorite candidate is eliminated — be transferred to
the front-runners of this party (Gallagher, 1980, 1988a; Goldman, 1930;
Katz, 1981; Mair, 1987a, 1987b; Marsh, 2000). Furthermore, many voters
give their first preference to their favorite candidate (primacy of locality over
party) and their lower preferences to the party of their favorite candidate
(primacy of party over locality) even when their favorite candidate has no
chance to be elected (Bowler, 1991a; Busteed, 1990; Gallagher, 1980,
1988a; Garvin, 1976; Katz, 1981; Mair, 1986, 1987a, 1987b; Marsh, 2000);
in extreme cases, this voting behaviour makes a party nominate more
candidates than there are seats in this constituency (Mair, 1986).
A larger number of candidates is also needed when vacant seats are filled
by recounts (That means: When a seat gets vacant then this seat is filled by
counting the ballots of the last regular elections anew, but with the current
members of parliament “immune to elimination” and with the ineligible
candidates ignored.) because otherwise there is the danger that this party
loses a seat to another party when this seat gets vacant and is filled by a
recount; the common tactic is to nominate to each candidate who gets a
bailiwick a sufficiently large number of running mates.
Example: A party uses vote management to win X = 5 seats. The party
believes that the same seat will get vacant not more than Y = 2 times. Then
this party will nominate X·(Y+1) = 15 candidates ( = 5 candidates a1, b1, c1,
d1, e1 and 10 running mates a2, b2, c2, d2, e2, a3, b3, c3, d3, e3 ). It will divide
the district into 5 bailiwicks. In the first bailiwick, it will ask its supporters to
vote a1 v a2 v a3 v b1 v b2 v b3 v c1 v c2 v c3 v d1 v d2 v d3 v e1 v
e2 v e3; in the second bailiwick, it will ask its supporters to vote b1 v b2 v
b3 v c1 v c2 v c3 v d1 v d2 v d3 v e1 v e2 v e3 v a1 v a2 v a3; in the
third bailiwick, it will ask its supporters to vote c1 v c2 v c3 v d1 v d2 v
d3 v e1 v e2 v e3 v a1 v a2 v a3 v b1 v b2 v b3; in the fourth bailiwick,
it will ask its supporters to vote d1 v d2 v d3 v e1 v e2 v e3 v a1 v a2 v
a3 v b1 v b2 v b3 v c1 v c2 v c3; and in the fifth bailiwick, it will ask its
supporters to vote e1 v e2 v e3 v a1 v a2 v a3 v b1 v b2 v b3 v c1 v c2
v c3 v d1 v d2 v d3. Advantages of this strategy are: (1) A direct
confrontation between a candidate and his running mates is prevented.
(2) When a representative is replaced by his running mate, then it is still
clear which representative represents which bailiwick, so that there is no
need to redraw the bailiwicks for the next regular elections.
24
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Thus, STV suffers from the same overnomination and undernomination
problems as cumulative voting, limited voting, and SNTV. However, these
problems are less severe under STV than under other multi-winner election
methods since Droop proportionality guarantees a minimum representation
for each party.
4.4. Criteria
The third problem is: According to which criteria should the electorate be
divided?
Usually the electorate is divided according to geographic or social
criteria. However, sometimes the electorate is divided according to the ID
numbers. Example: In 1997, two organizations, the Specialists and the
Initiative, ran for the two students’ seats of the Communication and
Historical Sciences Department of the Berlin University of Technology. The
Specialists ran a single list. The Initiative ran two lists; its first list was
named “Even List” and its second list was named “Odd List”. In its
newspaper and during campaign speeches, the Initiative asked its supporters
to vote for the Even List when their matriculate number was even and for the
Odd List when their matriculate number was odd. The reason for this
strategy was that this council was elected by the largest remainder method of
proportional representation by party lists; if the Initiative had run only one
list then it would have had to get more than three fourths of the votes to win
both seats; however, with two lists and a sufficiently even distribution of its
votes the Initiative needed only more than two thirds of the votes to win both
seats. In the end, the Even List got 129 votes and the Odd List got 110 votes;
with this vote management strategy the Initiative won both students’ seats.
When N = 239 votes are distributed in a random manner x:y (here x = y = 1),
then the standard deviation is (√(N·x·y))/(x+y) = 8. Therefore, the division of
the supporters was as even as statistically possible.
In Taiwan, the electorate is sometimes divided according to the birthdays.
Liu (1999) writes about the SNTV elections in Taiwan:
“The two opposition parties in Taiwan, the Democratic Progressive
Party (DPP) and the two-year-old New Party (NP), adopted a new
device to allocate their potential votes among their nominees in the
election of 1995. By placing advertisements in newspapers and
making announcements during campaign speeches, both parties asked
their supporters to cast votes according to their birth months. Since the
DPP nominated four candidates in the South District of Taipei City,
the DPP divided voters into four groups: those who were born in
January, February, and March; those who were born in April, May,
and June; and so on. Each group was asked to vote for one candidate.
The NP did the same thing. It nominated six candidates in the two
districts in Taipei, three in each. It accordingly divided the voters into
three groups using the same approach as the DPP. The aim of this
tactic was to allocate the party’s voters evenly among its nominees.
Both parties evidently assumed that the identification of their
supporters with each party was strong enough to induce them to vote
as the party instructed. The final results support this speculation.”
In Taipei South, the DPP got N = 211,559 votes; with x = 1 and y = 3 the
standard deviation is 199; however, the candidates got 56,848, 56,364,
50,072 resp. 48,275 votes. In Taipei North, the NP got N = 171,667 votes;
with x = 1 and y = 2 the standard deviation is 195; however, the candidates
25
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
got 61,259, 59,575 resp. 50,833 votes. In Taipei South, the NP got N =
167,938 votes; with x = 1 and y = 2 the standard deviation is 193; however,
the candidates got 60,485, 54,456 resp. 52,997 votes. Therefore, the
deviations are significantly larger than expected for a purely random
distribution. Possible explanations are the different lengths of the months
and perhaps an uneven distribution of the birthdays over the calendar days.
However, the most probable explanation is that the candidates were
differently popular; deviations caused by different popularities can be
circumvented by using asymmetric vote management (section 4.6).
There is the tendency that candidates get more votes when they are listed
higher on the ballot, even when the candidates are listed in an alphabetic
manner or in a random manner on the ballot (alphabetic voting; donkey
voting) (Bakker, 1980; Chen, 1994; Darcy, 1990, 1993; Hermens, 1968;
Kelley, 1984; Kestelman, 2002; Robson, 1974; Sowers, 1934). To minimize
this so-called ballot position effect some countries use Robson rotation. That
means: Starting with a ballot on which the candidates are listed in an
alphabetic manner, the list of candidates on the other ballots is changed in a
cyclic manner so that each candidate is on the top of the same number of
ballots; ballots with the same candidate on top are distributed evenly over
the constituency (Hughes, 2000). In Tasmania, the candidates are listed on
the ballot according to their party label; candidates with the same party label
are listed in an alphabetic manner; among candidates with the same party
label Robson rotation is being used. Therefore, the electorate can be divided
into bailiwicks simply by asking the voters to rank the candidates in the
same manner in which they are listed on the ballot. This vote management
strategy has been predicted; but it has not yet been observed (Farrell, 1996,
2000, 2006).
When the electorate is sufficiently small (e.g. when the upper house is
elected by an electoral college using STV), then the electorate can be divided
into bailiwicks in a completely arbitrary manner. For example, Braunias
(1932) and Sternberger (1969) write about the indirect elections to the upper
house (Landsting) of Denmark in 1866–1953:
“The seats are distributed according to Andrae’s method. However,
this method is not used in practice. The parties rather divide their
electors into groups so that each group contains a quota of members.
Each group writes on their ballots the name of only one Landsting
member and the names of three substitutes.”
The above statement (“The seats are distributed according to Andrae’s
method. However, this method is not used in practice.”) does not make much
sense. I guess that Braunias (1932) and Sternberger (1969) want to say that
no transfer of votes occurs. However, it is necessary to keep in mind that the
Andrae method does not transfer votes of eliminated candidates and it
transfers surpluses only when the elected candidate has more than an
Andrae-Hare quota N/M of votes. As a candidate is certain to be elected
already when he has more than N/(M+1) votes (even when the Andrae-Hare
quota is being used), the use of the Andrae-Hare quota in Denmark made
STV very prone to free riding strategies and vote management strategies.
In most cases, more than one criterion is used to divide the electorate into
bailiwicks. For example, Sacks (1970) writes that, in the Donegal North-East
constituency, Fine Gael gave its candidate Bertie Boggs not only a
geographic part of the constituency but also the Protestant voters of the other
26
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
parts of this constituency. Winters (2001) and Pitkin (2001) write that in
Cambridge, Massachusetts, the voters are always divided according to a
wide range of criteria simultaneously (Winters: “mix of issue-based,
geography-based, and identity-based”; Pitkin: “ideological, geographic,
ethnic, or familiar factions”).
4.5. Strictness
The fourth problem is: How strict should the division into bailiwicks be?
Marsh (2000) writes:
“Once the candidates are selected, the issue of running their
individual campaigns to best joint advantage is likely to cause some
difficulty. There are three ways to handle this. The first is the
‘anarchy’ option: do nothing, and allow each candidate to campaign
across the whole constituency and let matters take their course.
Conflict often arises between candidates competing for the same first
preference votes. This can be handled by the second option:
‘bailiwicking’. Here, each candidate is allocated a particular area of
the constituency within which their campaign should be concentrated.
Deals may be made about the extent to which any candidate is
allowed, on certain days, out of a particular ‘bailiwick’ but essentially
the solution consists of an agreement (or injunction) for the candidates
to stay apart from one another. In many cases a weak ‘bailiwick’
system is agreed where the candidates agree to stay out of each other’s
‘home’ areas but the remainder of the constituency is open to all. Such
arrangements may avoid conflict, or at least constrain it, but it does
not necessarily lead to an efficient outcome for the national party. The
system may produce a fairly even division of votes between a party’s
candidates (Farrell, 1996) but variations in the strength of a party’s
candidates, and the strength of the opposition’s candidates make it
very uncertain. The third solution is direct ‘vote management’. Here
the objective is to divide the vote up between the candidates so as to
maximise the number of seats obtained. The need, or opportunity for
such a strategy is the fact that preferences can only be transferred to a
candidate who remains in the race. A party’s candidates may
sometimes win enough votes to expect two seats but fail to get them
because too many votes go to one candidate and the second is
eliminated before those votes can be transferred, or finishes as runnerup when the first candidate has votes to spare. Equalising votes
between candidates is a difficult operation. It requires a fairly accurate
assessment of the party’s overall voting strength, both in terms of first
and later preferences. (Local polling has been used, particularly in
Fine Gael, to provide information in this respect.) It requires a set of
voters who are willing to vote for the candidate that they are advised
by the local party to vote for. And it requires the stronger candidate to
give up votes by advising supporters to vote for a running mate — and
risk defeat in the process. It does happen. In a notable case former
Fine Gael party leader Garret FitzGerald succeeded in winning two
seats in his constituency in 1989 by advising many of his supporters to
vote for his running mate, on the assumption that FitzGerald could
pick up transfers from all parties. The ploy succeeded, but only just.
Gallagher (1993a) estimated that in 1992 Fianna Fáil could have won
nine more seats with perfect vote management, Fine Gael two and
Labour one (plus a couple more where it should have run more
candidates), and similar tales could be told about missed opportunities
27
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
in other elections. Generally it seems such management can be
undertaken only with the active support of the stronger candidate(s).
National party executives lack the authority to impose it but Farrell
(1993) argues the practice has become more widespread in recent
years.”
Bowler (1991b) writes:
“In response to these pressures candidates from the same party may
draw up an agreement which restricts campaigning for first
preferences to geographically restricted areas. These contracts vary in
both specificity and formality. In the Wexford constituency in 1989,
for example, the Fine Gael candidates drew up a formal Code of
Conduct which divided up the constituency into areas over which each
candidate had sole right of campaigning. Each Fine Gael candidate in
Wexford was also allotted two days in which to campaign across the
entire constituency. This type of campaigning will overlap with, and
may even be the main basis of, ‘friends and neighbours’ effects. The
point here is that it also provides incentives for candidates from within
the same party to cheat on such agreements and so engage in a
campaign against fellow party members. Candidates from within the
same party, then, can be seen to contribute to the usual fissiparous
effect of PR upon party unity and stability. The importance of intraparty competition in terms of voter choice is seen when we note that
in 1982, for instance, 17 of the 25 sitting Fianna Fáil deputies who lost
did so to members of their own party; for Fine Gael, this figure was 5
out of 12.”
4.6. Symmetry
The fifth problem is: Should the candidates get bailiwicks of same size or
of different size?
When the candidates get bailiwicks of same size, then this is called
symmetric vote management; otherwise, this is called asymmetric vote
management. There are mainly three reasons why candidates should get
bailiwicks of different size. First: In Ireland, the constitution says (1) that the
Prime Minister (Taoiseach), the Deputy Prime Minister (Tánaiste), and the
Minister of Finance have to be members of the lower house, (2) that all other
Cabinet Ministers have to be members of the lower house (Dáil) or the upper
house (Seanad), and (3) that not more than two Cabinet Ministers can be
members of the Seanad; however, by tradition, all Cabinet Ministers and all
Junior Ministers have to be members of the Dáil. In Malta, the constitution
says that all Cabinet Ministers have to be members of the unicameral
parliament. Therefore, it is necessary to make the election of those about 30
candidates (Ireland) resp. those about 15 candidates (Malta) who are
designated for government offices certain; as the coalition usually has only
about 80 seats (Ireland) resp. about 35 seats (Malta) and as STV makes
every seat vulnerable, it is very difficult to make the election of a given
candidate certain. Because of these regulations resp. because of similar
regulations in other countries (For example: In some communities in the
USA, it was tradition that that candidate, who has been elected at the earliest
stage of the count resp. — when more than one candidate has been elected at
this stage — of all those candidates who have been elected at this stage that
candidate who has got the largest surplus at this stage, becomes mayor
(Amy, 1993).), those candidates, who are designated for government offices,
usually get larger bailiwicks.
28
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
However, also the opposite tendency can be observed: As these
regulations make voters vote preferably for candidates who are designated
for government offices (because voters have an interest that government
officials come from their constituency and because these regulations mean
that these candidates necessarily have to be elected into the parliament to be
able to get government offices), such candidates need only a smaller
bailiwick. This voting behaviour is strengthened by the fact that, in the ideal
case, an additional vote for candidate a of party X helps party X win an
additional seat only when candidate a gets this additional seat. This voting
behaviour can best be observed in those constituencies where a given party
cannot hope to win more than one seat, because here this voting behaviour
cannot be attributed to asymmetric vote management. Busteed (1990) writes:
“It has already been noted how in June 1981 North Kerry elected
the Labour TD Dick Spring, but he only took the seat on the sixth and
last count with the narrow margin of 144 votes over his Fine Gael
opponent. Subsequently he was appointed Minister of State at the
Department of Justice, and his electoral position was transformed. In
the February 1982 general election he topped the poll and was elected
on the first count with 25.8% of first preferences. Recent injury in a
car crash may also have pulled in sympathy votes. By November 1982
he was Labour leader and clearly destined to be Tánaiste in any future
coalition. The prospect improved his position still further: again he
topped the poll, this time with 28.9% of first preferences. The
explanation for his success may have lain in pride at a local boy made
good, but it seems equally likely that the electors of North Kerry were
drawn to him by the expectation that from his increasingly powerful
position he could divert a good deal of patronage to the constituency
and by their votes they simultaneously strengthened his base and
established a claim on him. (...)
The belief is that the promotion of a TD will in a broad sense
flatter constituency pride. Voters for their party will both bask in
reflected glory and expect that their representatives’ extra pull will
now be deployed to the community’s material advantage when it
comes to the allocation of public resources. Such considerations are
widely believed to be particularly influential in the appointment of the
junior ministers known as Ministers of State. Such posts it is
suggested are sometimes allocated to TDs who won marginal seats in
the hope that this will consolidate their positions at the next election.
For example, in the 1981 coalition government Michael Begley, Fine
Gael TD for Kerry South was appointed Minister of State for Trade,
Commerce, and Tourism. He was the only party deputy in either Kerry
constituency and his seat seemed vulnerable since his first preference
vote had fallen by over 500 compared with the 1977 election and he
had only been elected at the fourth count. If his appointment was
designed to strengthen his position it succeeded since he was reelected comfortably in both February and November 1982, his share
of first preferences rising from 18.3% through 20.8% to 22.8%.”
Second: Especially at universities and in private organizations, but also in
public elections, frequently the bylaws require that each social group must
be represented by a minimum number of seats. This is called “STV with
constraints” (Hill, 1998, 1999; Kitchener, 1999; Otten, 2001). For example,
the constitution of Edmonton, Alberta, said that at least 3 of the 7 members
of the City Council have to come from the Strathcona borough (Hoag, 1926;
Johnston, 2000). Such a regulation is fulfilled by declaring a candidate
29
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
“immune to elimination” when his elimination would lead to a violation of
this regulation. The consequence of such a regulation is that in a vote
management strategy candidates who are believed to become “immune to
elimination” get a bailiwick which is only as large as necessary to guarantee
that these candidates still become “immune”.
The same phenomenon occurs when all voters of a given minority strictly
prefer each candidate of this minority to each other candidate, independent
of the party labels of the candidates (religious voting; racial voting). For
example, Protestant voters usually strictly prefer each Protestant candidate to
each other candidate (Busch, 1995; Gallagher, 1980; Moley, 1918; Sacks,
1970); the same is valid for Afro-Americans (Burnham, 1990, 1997;
Goldman, 1930; Gosnell, 1930; Harris, 1930), Poles (Anderson, 1995;
Moley, 1923), Italians (Busch, 1995; Moscow, 1967), etc.. When it is clear
in advance that a given minority will win Mp seats, then it is sufficient that
the candidates of this minority get only bailiwicks of Np/(Mp+1) voters,
where Np is the number of voters of this minority. When e.g. Np is slightly
larger than a Droop quota N/(M+1), then it is sufficient that the bailiwick of
the candidate of this minority is slightly larger than a half Droop quota; at
each stage of the count, this candidate of the minority will have more votes
than every other candidate of this minority so that he will get the votes of the
other candidates.
Third: As popular candidates usually win more additional votes during
the transfer of votes than unpopular candidates do, popular candidates
sometimes get smaller bailiwicks. In the above quotation by Marsh (2000),
Garret FitzGerald did not get any bailiwick at all since his party, the Fine
Gael, expected that he will win so many additional votes during the count
that he did not need any bailiwick at all. With this strategy, the Fine Gael,
which had won only one of the 4 seats of the Dublin South-East constituency
with 32.0% of the first preferences in 1987 (FitzGerald: 21.1%; Joseph
Doyle: 8.7%; William Egan: 2.2%), won 2 of the 4 seats with 27.7% in 1989
(Doyle: 15.9%; FitzGerald: 11.7%) (Gallagher, 1990a). On the other side, as
sometimes popular candidates are willing to participate at a vote
management strategy only when their re-election is not put in danger by this
strategy, these candidates sometimes get a larger bailiwick (Marsh, 2000).
Bailiwicks of different size are also necessary when the strengths of the
opposition’s candidates differ too much (Marsh, 2000). In the end, the size
of the bailiwick of a given candidate depends mainly on his interests and on
his ability to get his way (Mair, 1987a, 1987b).
Example: In 1973, the Fianna Fáil won only one of the 3 seats in the
Sligo-Leitrim constituency with 50.6% of the first preferences (Raymond
McSharry: 25.8%; Bernard M. Brennan: 16.9%; Joseph Mary Mooney:
8.0%). To win 2 seats in 1977, Fianna Fáil decided to use vote management.
As McSharry was willing to participate at this vote management only when
this did not risk his re-election, this constituency was not divided 1:1 but 2:1,
where McSharry got the larger part and James Gallagher got the smaller part.
Although the vote share of the Fianna Fáil dropped from 50.6% in 1973 to
48.0% in 1977, it could win 2 of the 3 seats with this vote management. Mair
(1986) writes:
“A good example of such a division of territory is afforded by the
Sligo-Leitrim constituency in 1977, where Fianna Fáil was attempting
to win two seats in a very marginal 3-seat constituency. The
constituency was dominated by one major urban center, Sligo town,
and was otherwise a predominantly rural area. One of the two Fianna
Fáil candidates (McSharry) based his support in Sligo town, while the
30
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
other (Gallagher) was based southern end of the county, a mainly
farming area with small market towns such as Ballymote, Colooney,
and Tubbercurry (Gallagher’s home town). In this particular case, the
bailiwicking was easily effected: McSharry had the town and coastal
strip, or what he referred to as the area ‘from Bundoran to Ballina,
between the mountains and the sea,’ while Gallagher had the
remaining and admittedly smaller part of the constituency. In the
former area the Fianna Fáil posters urged supporters to ‘vote No. 1
McSharry and No. 2 Gallagher,’ and in the latter ‘vote No. 1
Gallagher and No. 2 McSharry.’ A border was clearly delineated by
both candidates, and so the contest was organized. In the event, Fianna
Fáil did win two of the three seats with an overall vote of 48.0%
(30.8% for McSharry and just 17.3% for Gallagher), and with over
72% of McSharry’s surplus passing to Gallagher in the second count.”
Of course, the above mentioned vote management strategies can be
combined in many different manners. For example, Galligan (1999) writes
that in the elections to the Dáil in 1997 the Fianna Fáil divided the 4-seat
Longford-Roscommon constituency 2:3 where the smaller part went to the
TD and former Taoiseach Albert Reynolds while the larger part went to the
candidates Seán Doherty, Michael Finneran, and Terry Leyden. This is not
only an example for asymmetric vote management (as the constituency was
divided 2:3 and not 1:3), but also for differently strict divisions. In these
elections, Reynolds got 39.3%, Doherty 25.9%, Finneran 19.9%, and Leyden
14.9% of all first preferences of the Fianna Fáil. Reynolds and Doherty were
elected while Finneran and Leyden were eliminated. With 47.0% of all first
preferences the Fianna Fáil won 2 of the 4 seats; therefore, it did not win
more seats than it would have won without this vote management strategy;
however, this vote management strategy guaranteed that Reynolds was
among the elected Fianna Fáil candidates.
4.7. Summary
Vote management is a strategy where a party or a group of independent
candidates asks its supporters to vote preferably for those of its candidates
who are less assured of election.
Vote management is neither an invention of the 1970s or 1980s nor a
pure Irish phenomenon. The political organizations rather understood the
usefulness of vote management almost immediately. But it always took very
much experience until they were able to run vote management successfully.
Especially, it took very much time until they observed that it is usually not
useful to divide the electorate into bailiwicks of same size.
Today, its vulnerability to vote management strategies is STV’s most
serious problem. The Royal Commission on the Electoral System (New
Zealand 1986), the Plant Commission (UK 1993), and the Jenkins
Commission (UK 1998) rejected STV partly because of Ireland’s bad
experience with vote management. Vote management also has a bad
influence on intra-party democracy: Frequently, candidates complain that
their party did not allow them to campaign in the whole constituency
(McDaid, 1993; Sacks, 1970). Other authors call vote management
“corrupting” (Kestelman, 2000) and compare the Irish parties with the “party
machines” (Bax, 1973) in the USA or even with the “Mafia” (Sacks, 1976).
Therefore, each attempt to find better STV methods should primarily try to
reduce its vulnerability to vote management.
31
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
5. Proportional Completion
In sections 6 and 7, we will restrict our considerations to situations where
each voter v ∈ V casts a linear order v on A. Therefore, we have to explain
how non-linear individual orders are completed to linear individual orders
when some voters cast non-linear orders.
The common way to complete non-linear individual orders to linear
individual orders is symmetric completion. Symmetric completion means:
When voter v ∈ V is indifferent between the candidates f1,...,fn ∈ A, then this
voter is removed from V and, for each of the n! possible permutations
{σ(1),...,σ(n)} of {1,...,n}, a voter u is added to V who has the weight 1/(n!),
who ranks the candidates fσ(1) u ... u fσ(n), and who ranks the other
candidates relatively to each other in the same manner as voter v did.
However, a problem with symmetric completion is that adding an empty
ballot and completing this ballot in a symmetric manner can change the
result of the elections. Also adding a voter, who prefers a very weak
candidate (resp. a very strong candidate) to every other candidate and who is
indifferent between every other candidate, and completing his ballot in a
symmetric manner can change the result of the elections. One would expect
that adding a voter, who is indifferent between all those candidates whose
election is unclear, doesn’t change the result of the elections.
Because of these reasons, we propose proportional completion as an
alternative to symmetric completion. Proportional completion means that
non-linear individual orders are completed to linear orders in such a manner
that, for each set of candidates, the proportions of the (to these candidates
restricted) individual orders are not changed. So when Nempty voters, who are
all indifferent between all those candidates f1,...,fn ∈ A whose election is
unclear, are added, then proportional completion simply means that, for each
linear order of the candidates f1,...,fn ∈ A, the number of ballots with this
order is multiplied by 1 + Nempty/Nold.
Example 1: Suppose a voter is indifferent between candidate a and
candidate b. Suppose of the other voters X1 = 56 strictly prefer candidate a to
candidate b and X2 = 44 strictly prefer candidate b to candidate a, then this
voter is replaced by X1/(X1+X2) = 0.56 voters who rank these candidates
a v b and by X2/(X1+X2) = 0.44 voters who rank these candidates b v a and
who rank the other candidates in the same manner as the original voter did.
Example 2: Suppose a voter is indifferent between the candidates a, b, c,
and d. Suppose X > 0 voters are not indifferent between these candidates.
Suppose X1 voters rank these candidates a ≈v c v b ≈v d, X2 voters rank
them d v a ≈v b ≈v c, X3 voters rank them c ≈v d v b v a, etc.. Then this
voter is replaced by X1/X voters who rank them a ≈v c v b ≈v d, X2/X voters
who rank them d v a ≈v b ≈v c, X3/X voters who rank them c ≈v d v b v a,
etc. and who rank the other candidates in the same manner as the original
voter did. At additional stages, these still incomplete individual orders are
further completed.
32
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
5.1. Definition of Proportional Completion
The following 3 stages give a precise definition for proportional
completion.
Stage 1:
W shall be the proportional completion of V. ρ(w) ∈  shall be the
weight of voter w ∈ W. Then we start with
(a)
W : = V.
(b)
∀ w ∈ W: ρ(w) : = 1.
Stage 2:
Suppose there is a voter w ∈ W and a set of candidates f1,...,fn ∈ A with
(a)
n > 1.
(b)
∀ fi,fj ∈ {f1,...,fn}: fi ≈w fj.
(c)
∀ fi ∈ {f1,...,fn} ∀ e ∈ A \ {f1,...,fn}: fi w e.
Suppose X ∈ 0 is the number of voters v ∈ V with
(5.1.1)
∃ fi,fj ∈ {f1,...,fn}: fi v fj.
Case 1: X > 0.
For each voter v ∈ V with (5.1.1), a voter u is added to W with
(5.1.2)
∀ g,h ∈ A \ {f1,...,fn}: g w h ⇔ g u h.
(5.1.3)
∀ fi ∈ {f1,...,fn} ∀ g ∈ A \ {f1,...,fn}: g w fi ⇔ g u fi.
(5.1.4)
∀ fi ∈ {f1,...,fn} ∀ h ∈ A \ {f1,...,fn}: fi w h ⇔ fi u h.
(5.1.5)
∀ fi,fj ∈ {f1,...,fn}: fi v fj ⇔ fi u fj.
(5.1.6)
ρ(u) : = ρ(w) / X.
Case 2: X = 0.
For each of the n! possible permutations {σ(1),...,σ(n)} of
{1,...,n}, a voter u is added to W with (5.1.2) – (5.1.4) and
(5.1.7)
∀ fi,fj ∈ {f1,...,fn}: σ(i) > σ(j) ⇔ fi u fj.
(5.1.8)
ρ(u) : = ρ(w) / (n!).
After all these voters u have been added to W, the original voter w is
removed from W.
Stage 3:
Stage 2 is repeated until a w b ∀ a ∈ A ∀ b ∈ A \ {a} ∀ w ∈ W.
33
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
6. A New STV Method
In sections 3 and 4, we saw that today Hylland free riding and vote
management are the two most serious problems of STV methods. In this
section, we introduce a mathematical model to describe vote management
(section 6.1). In section 6.2, we use this model to design an STV method that
is vulnerable to Hylland free riding and vote management only in those cases
in which otherwise Droop proportionality would have to be violated.
6.1. Equivalence of Free Riding and Vote Management
In sections 3 and 4, we explained why today Hylland free riding and vote
management are the two most serious problems of STV methods.
Nevertheless, we are aware of only a few papers that try to explain which
property of STV methods is that property that is misused in a vote
management strategy. For example, Hylland (1992) writes:
“Since candidates can be elected with fewer votes than the quota,
there are cases in which a group can gain by dividing the first
preferences of its supporters evenly among its candidates, securing
each of them fewer than the quota, but enough to be elected.”
Farrell (2006) writes:
“It is generally argued in the literature that parties aiming to
maximise the number of seats they win should try to spread the
preferences as evenly as possible among their candidates, to give all
their candidates a good chance of remaining in the count long enough
to pick up preferences from other parties. An inappropriate distribution
of the preference vote between candidates of the same party can lead
to that party losing an otherwise winnable seat. As Cox (1997) put it,
the parties should try to redirect votes from ‘vote-rich’ to ‘vote-poorer’
candidates. According to Gallagher (1992): ‘Under the assumption that
no votes transfer across party lines, a party’s ideal strategy under STV
is to ensure that all of its candidates have exactly the same number of
votes at every stage of the count, and that when any one is eliminated,
his or her votes transfer evenly among the party’s other candidates.’”
According to Marsh (2000), a vote management strategy misuses the fact
that “preferences can only be transferred to a candidate who remains in the
race” and according to Hylland a vote management strategy misuses the fact
that, because of ballots that have become exhausted, “candidates can be
elected with fewer votes than the quota”. Marsh’s and Hylland’s conjectures
are problematic because of two reasons. First: The fact that preferences
cannot be transferred to already eliminated candidates and the fact that
candidates can be declared elected without reaching the quota are rather
parts of the description of the counting process of traditional STV methods
than a property of these STV methods. In other words, whether a given STV
method is vulnerable to vote management strategies must not depend on
whether this STV method is defined in an axiomatic manner or an
algorithmic manner. Second: Their conjectures cannot explain why in multiwinner elections spreading the preferences evenly among the party
candidates is a useful strategy even when no elimination of candidates and,
therefore, also no exhaustion of ballots occur.
34
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Example 1 ( N = 100 voters; M = 2 seats; C = 3 candidates ):
10 voters
35 voters
25 voters
30 voters
a v b v c
a v c v b
b v c v a
c v b v a
In example 1, the winners are the candidates a and c. However, when the
candidates a and b run a vote management strategy against candidate c and
ask their supporters to vote preferably for candidate b then this example
looks as follows:
Example 2 ( N = 100 voters; M = 2 seats; C = 3 candidates ):
10 voters
35 voters
25 voters
30 voters
b v a v c
a v c v b
b v c v a
c v b v a
Now, the winners are the candidates a and b. The fact that vote
management is possible although only 3 candidates are running for 2 seats so
that no elimination of candidates and, therefore, also no exhaustion of ballots
occur demonstrates that none of these properties can be that property that is
misused in a vote management strategy.
This example demonstrates that also (1) the special rules to transfer
surpluses or (2) the violation of monotonicity cannot be that property of STV
methods that is misused in a vote management strategy.
Presumption of this paper is that the vulnerability to Hylland free riding
is that property of STV methods that is misused in a vote management
strategy. To be more concrete: We presume that the term “Hylland free
riding” and the term “vote management” refer to the same strategic problem.
The only difference is that the term “Hylland free riding” refers to this
strategic problem seen from the point of view of an individual voter who
tries to maximize the influence of his vote by voting preferably for those of
his favorite candidates who are less assured of election, while the term “vote
management” refers to a political party or a group of independent candidates
that tries to maximize its number of seats by asking its supporters to vote
preferably for those of its candidates who are less assured of election.
Consequences of this presumption are (1) that an election method is
vulnerable to vote management if and only if it is vulnerable to Hylland free
riding and (2) that an election method is the more vulnerable to vote
management the more vulnerable it is to Hylland free riding.
The example with Garret FitzGerald ( sections 4.5 and 4.6 ) demonstrates
that, for voter v to participate at a vote management strategy of the
candidates a1,...,aM against candidate b, it is sufficient that voter v prefers that
candidate ak, for which this voter has to vote in this vote management
strategy, to candidate b. It is not necessary that this voter prefers all the
candidates a1,...,aM to candidate b. Otherwise, only those voters had voted for
Joseph Doyle who prefer both, Doyle and FitzGerald, to the other candidates.
Therefore, we get the following general results: When the used multiwinner election method satisfies Droop proportionality and each voter casts
35
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
a linear order v on A, then vote management of the candidates a1,...,aM
against candidate b is possible if and only if there is a t ∈ (N×M) with
properties (6.1.1) – (6.1.4).
(6.1.1)
∀ i ∈ {1,...,N} ∀ j ∈ {1,...,M}: tij ≥ 0.
(6.1.2)
∀ i ∈ {1,...,N}:
∑t
M
ij
≤ 1.
j =1
(6.1.3)
∀ i ∈ {1,...,N} ∀ j ∈ {1,...,M}: b i aj ⇒ tij = 0.
(6.1.4)
∀ j ∈ {1,...,M}:
∑t
N
ij
> N/(M+1).
i =1
The candidates a1,...,aM can then ask each voter i to give tij of his vote to
candidate aj. In so far as (6.1.3) says that tij can be larger than 0 only when
voter i prefers candidate aj to candidate b, it is guaranteed that voter i will be
willing to give tij of his vote to candidate aj. (6.1.4) says that each of the
candidates a1,...,aM will then have more than N/(M+1) votes and will
necessarily be elected according to Droop proportionality.
If there is a t ∈ (N×M) with properties (6.1.1) – (6.1.3) and (6.1.5), then
the candidates a1,...,aM can run a vote management strategy against candidate
b with the aim that candidate b is, at best, tied for election:
(6.1.5)
∀ j ∈ {1,...,M}:
∑t
N
ij
≥ N/(M+1).
i =1
A Condorcet candidate is a candidate b ∈ A such that there is no set of
candidates {a1,...,aM} ∈ AM such that there is a t ∈ (N×M) with properties
(6.1.1) – (6.1.3) and (6.1.5).
So when we want to minimize the vulnerability to vote management and
Hylland free riding, we should insist that, if candidate b ∈ A is a Condorcet
candidate, then candidate b is in every winning set M.
36
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
6.2. Definition of the Schulze STV Method
In this section, we propose new STV method, where the vulnerability to
Hylland free riding and vote management is minimized.
Stage 1:
Proportional completion is used to complete V to W.
Suppose NW is the number of voters in W.
Suppose ρ(w) ∈  with ρ(w) > 0 is the weight of voter w ∈ W.
Stage 2:
A path from set X ∈ AM to set Y ∈ AM is a sequence of sets
C(1),...,C(n) ∈ AM with the following properties:
1.
2.
3.
4.
X ≡ C(1).
Y ≡ C(n).
2 ≤ n < ∞.
For all i = 1,...,(n–1): C(i) and C(i+1) differ in exactly one
candidate. That means: | C(i) ∩ C(i+1) | = M – 1 and
| C(i) ∪ C(i+1) | = M + 1.
Suppose a1,...,aM,b ∈ A. Then N[{a1,...,aM},b] ∈  is the largest value
such that there is a t ∈ (NW×M) such that
(6.2.1)
∀ i ∈ {1,...,NW} ∀ j ∈ {1,...,M}: tij ≥ 0.
(6.2.2)
∀ i ∈ {1,...,NW}:
∑t
M
ij
≤ ρ(i).
j =1
(6.2.3)
∀ i ∈ {1,...,NW} ∀ j ∈ {1,...,M}: b i aj ⇒ tij = 0.
(6.2.4)
∀ j ∈ {1,...,M}:
NW
∑t
ij
≥ N[{a1,...,aM},b].
i =1
If X,Y ∈ AM differ in exactly one candidate, then we define Ñ[X,Y] : =
N[{a1,...,aM},b] with X = {a1,...,aM} and b = Y \ X.
The strength of the path C(1),...,C(n) is
min { Ñ[C(i),C(i+1)] | i = 1,...,(n–1) }.
In other words: The strength of a path is the strength of its weakest link.
P[A,B] : = max { min { Ñ[C(i),C(i+1)] | i = 1,...,(n–1) }
| C(1),...,C(n) is a path from set A to set B }.
In other words: P[A,B] is the strength of the strongest path from set
A ∈ AM to set B ∈ AM \ {A}.
(6.2.5)
The binary relation M on AM is defined as follows:
AB ∈ M : ⇔ P[A,B] > P[B,A].
(6.2.6)
M : = { A ∈ AM | ∀ B ∈ AM \ {A}: BA ∉ M } is the set
of winning sets.
37
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Stage 3:
1 is calculated as defined in (6.2.5).
For all A,B ∈ M: Suppose there is a candidate a ∈ A \ B with ab ∈  1
for every candidate b ∈ B \ A, then the set A disqualifies the set B.
M ⊆ M, the winning sets of the Schulze STV method, is the set of all
those sets A ∈ M that are not disqualified by some other set B ∈ M.
The fact, that this method is well defined, has been shown by Schulze
(2011, section 4.1). The fact, that this method guarantees the election of
every Condorcet candidate is a direct consequence of the fact that N[{a1,...,
aM},b] < N/(M+1) for every {a1,...,aM} ∈ AM and every Condorcet candidate
b ∈ A.
6.3. Example
Example ( M = 3 seats; C = 5 candidates; N = 630 voters ):
60
45
30
15
12
48
39
21
27
9
51
33
42
18
6
54
57
36
24
3
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
a v b v c v d v e
a v c v e v b v d
a v d v b v e v c
a v e v d v c v b
b v a v e v d v c
b v c v d v e v a
b v d v a v c v e
b v e v c v a v d
c v a v d v b v e
c v b v a v e v d
c v d v e v a v b
c v e v b v d v a
d v a v c v e v b
d v b v e v c v a
d v c v b v a v e
d v e v a v b v c
e v a v b v c v d
e v b v d v a v c
e v c v a v d v b
e v d v c v b v a
In this example, we get:
N[{a,b,c},d] = 169;
N[{a,b,c},e] = 152;
N[{a,b,d},c] = 162;
N[{a,b,d},e] = 159;
N[{a,b,e},c] = 168;
N[{a,b,e},d] = 153;
N[{a,c,d},b] = 158;
N[{a,c,d},e] = 163;
N[{a,c,e},b] = 164;
N[{a,c,e},d] = 157;
N[{a,d,e},b] = 167;
N[{a,d,e},c] = 154;
N[{b,c,d},a] = 141;
N[{b,c,d},e] = 165;
N[{b,c,e},a] = 146;
N[{b,c,e},d] = 160;
N[{b,d,e},a] = 151;
N[{b,d,e},c] = 155;
N[{c,d,e},a] = 156;
N[{c,d,e},b] = 150.
38
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
159
162
Ñ[{abd},*]
162
Ñ[{abe},*]
168
153
168
153
Ñ[{acd},*]
158
158
163
163
Ñ[{ace},*]
164
Ñ[{ade},*]
167
Ñ[{bcd},*]
141
Ñ[{bce},*]
146
Ñ[{bde},*]
Ñ[{cde},*]
164
157
167
154
141
152
162
163
164
154
165
151
156
39
153
158
157
146
156
159
168
141
146
151
159
169
Ñ[*,{cde}]
152
Ñ[*,{bde}]
169
Ñ[*,{bce}]
Ñ[*,{ace}]
152
Ñ[*,{bcd}]
Ñ[*,{acd}]
169
Ñ[*,{ade}]
Ñ[*,{abe}]
Ñ[{abc},*]
Ñ[*,{abd}]
Ñ[*,{abc}]
The pairwise matrix Ñ looks as follows:
160
151
155
155
156
150
150
157
167
154
165
165
160
160
155
150
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
In the graph theoretical interpretation of the proposed election method,
each possible way to fill the M = 3 seats is represented by a vertex. There is
a link from vertex A to vertex B if and only if set A and set B differ in
exactly one candidate. The strength of the link from vertex A to vertex B is
Ñ[A,B]. Therefore, the following graphic represents the discussed example:
abc
abd
169
162
152
159
162
146
169
151
cde
152
159
152
168
153
abe
158
158
164
168
155
151
153
160
150
156
141
163
141 169
bde
168
150
154
156
146
acd
167
150
160
141
157
162
158
155
163
157
167 159
155
156
151
165
bce
164
153
154
146
164
163
160
165
154
157
165
167
bcd
ade
The following table lists the strongest paths. “A,x,B” means Ñ[A,B] = x.
The critical pairwise defeats of the strongest paths are underlined. Although
there can be more than one strongest path from set A ∈ AM to set
B ∈ AM \ {A}, the strength of the strongest path P[A,B] is well defined.
40
ace
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
The strongest paths are:
... to abc ... to abd ... to abe ... to acd ... to ace ... to ade ... to bcd ... to bce ... to bde ... to cde
from abc ...
---
abd,162,
from abd ...
abc
abc,169,
abc,169, abc,169,
abc,169, abc,169, abc,169,
abc,169, acd,163, abc,169,
abc,169,
acd,163, acd,163,
bcd,165, bcd,165, bcd,165,
abd
ade,167,
acd
bcd
ace
ade
bce
bde
cde
abe
---
abe,168,
abe,168,
abc,169,
from abe ...
abc
abd
abd,162,
abd,162, abd,162,
abd,162, abd,162, abd,162,
acd,163, abd,162,
abd,162,
acd,163, acd,163,
bcd,165, bcd,165, bcd,165,
ade,167,
acd
bcd
ace
ade
bce
bde
cde
abe
---
acd,163,
acd,163, acd,163,
ade,167,
ade,167, ade,167,
from acd ...
abe,168,
abd
abe
abc
abe,168,
abe,168, abe,168,
abe,168,
abe,168,
abe,168, abc,169,
abe,168, abc,169, abc,169,
abc,169,
abc,169,
acd,163,
bcd,165, bcd,165,
ace
bce
acd
bcd
ade
bde
cde
---
ace,164,
ace,164,
ace,164,
ace,164,
abc,169,
abc,169,
from ace ...
abc
abe
abd
acd
acd,163,
acd,163,
ade,167,
acd,163,
ade,167,
acd,163, acd,163,
acd,163,
abe,168,
ade,167,
abe,168,
ace
ade
cde
abc,169,
bde
bce
bcd
---
ade,167,
ade,167,
ade,167,
ade,167, ade,167, abe,168,
abe,168,
from ade ... abe,168,
abc,169,
abd
abe
abc
ace
acd
bcd,165,
cde,156,
from bcd ... ade,167,
abe,168,
abc
bce,160,
cde,156,
from bce ... ade,167,
abe,168,
abc
bde,155,
cde,156,
ade,167,
from bde ...
abe,168,
abc
ace,164,
ace,164, ace,164,
ace,164,
abc,169,
ace,164, abc,169, abc,169,
abc,169,
acd,163,
bcd,165, bcd,165,
bce
bcd
bde
cde
ade
---
bcd,165, bcd,165,
bcd,165, bcd,165, bcd,165,
cde,156, cde,156,
cde,156, cde,156, cde,156,
ade,167, ade,167,
acd
ace
ade
abd
abe
ade,167,
ade,167,
ade,167,
abe,168,
abe,168,
ade,167,
abe,168,
abc,169,
abc,169,
bde
bce
bcd,165,
bcd
cde
---
bce,160, bce,160,
bce,160, bce,160, bce,160,
cde,156, cde,156,
bce,160,
cde,156, cde,156, cde,156,
ade,167, ade,167,
bcd
acd
ace
ade
abd
abe
bcd,165, bcd,165, bcd,165,
bce
bde
cde
---
bde,155, bde,155,
bde,155, bde,155, bde,155,
cde,156, cde,156,
bde,155, bde,155,
cde,156, cde,156, cde,156,
ade,167, ade,167,
bcd
bce
acd
ace
ade
abd
abe
bce,160, bce,160,
bde
cde
---
cde,156,
cde,156,
cde,156,
cde,156, cde,156,
ade,167,
cde,156,
ade,167,
ade,167,
cde,156, cde,156, cde,156,
ade,167, ade,167,
abe,168,
ade,167,
from cde ...
abe,168,
abe,168,
acd
ace
ade
abd
abe
abc,169,
bde
abc
bce
bcd
41
bde,155,
cde
---
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
P[*,{abc}]
P[*,{abd}]
P[*,{abe}]
P[*,{acd}]
P[*,{ace}]
P[*,{ade}]
P[*,{bcd}]
P[*,{bce}]
P[*,{bde}]
P[*,{cde}]
Therefore, the strengths of the strongest paths are:
P[{abc},*]
---
169
163
169
163
163
169
165
165
165
P[{abd},*]
162
---
162
162
162
162
162
162
162
162
P[{abe},*]
168
168
---
168
168
163
168
168
165
165
P[{acd},*]
163
163
163
---
163
163
163
163
163
163
P[{ace},*]
164
164
164
164
---
163
164
164
164
164
P[{ade},*]
167
167
167
167
167
---
167
167
167
165
P[{bcd},*]
156
156
156
156
156
156
---
165
165
165
P[{bce},*]
156
156
156
156
156
156
160
---
160
160
P[{bde},*]
155
155
155
155
155
155
155
155
---
155
P[{cde},*]
156
156
156
156
156
156
156
156
156
---
A = {a,d,e} is the unique winning set, since it is the only set with P[A,B]
≥ P[B,A] for every other set B ∈ A3.
7. Proportional Rankings
When proportional representation by party lists is being used, then each
party has to submit in advance a linear order of its candidates without
knowing how many seats it will win. Frequently, the parties are interested
that — however many candidates are elected — the elected candidates
reflect the strengths of the different party wings in a manner as proportional
as possible (Otten, 1998, 2000; Rosenstiel, 1998; Warren, 1999b). We will
call a linear order with this property a proportional ranking. The two most
important suggestions to produce a proportional ranking are the bottom-up
approach (Rosenstiel, 1998) and the top-down approach (Otten, 1998, 2000).
The bottom-up approach says that we start with the situation where all C
candidates are elected. Then, for k = C to 2, we ask which candidate can be
eliminated so that the distortion of the proportionality of the still running
candidates is as small as possible; the newly eliminated candidate then gets
the k-th place of this party list.
The top-down approach says that we use a single-winner election method
to fill the first place of this party list. Then, for k = 2 to C, we ask which
candidate can be added to those candidates who have already got a place so
that the distortion of the proportionality is as small as possible; the newly
added candidate then gets the k-th place of this party list.
I prefer the top-down approach to the bottom-up approach, because the
bottom-up approach starts with the lowest and, therefore, (as the number of
42
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
candidates is usually significantly larger than the number of seats this party
can realistically hope to win) least important places so that slight fluctuations
in the filling of the lowest places can have an enormous impact on the filling
of the best places. Therefore, in this paper we presume that the top-down
approach is being used.
Although we are not aware of any empirical study on strategic voting
when producing a party list, we predict that Hylland free riding and vote
management are the most serious problems. In this context, Hylland free
riding means that a voter votes preferably for those of his favorite candidates
who are lower in the expected party list. Vote management means that a
group of candidates asks its supporters to vote preferably for those
candidates of this group who are lower in the expected party list. With this
strategy the stronger candidates get lower places than they would have got
otherwise, while the weaker candidates get better places than they would
have got otherwise; therefore, the aim of this strategy is that the stronger
candidates get places that are still good enough and that the weaker
candidates get places that are just good enough to get elected.
Actually, we predict that Hylland free riding and vote management are
significantly more serious problems when producing a party list than under
STV methods: The party organization must have an interest that the best
places of the party list are filled by those candidates with whom this party
wants to advertise in the election campaign. However, when the party
expects to win (say) 50 seats and when the voters use Hylland free riding
and vote management, then the best places of this party list are rather filled
by candidates of that party wing that happens to run the lousiest vote
management, because when a candidate gets one of the best places then this
means that the number of voters who voted for him was larger than
necessary to make him get just one of the best 50 places. Therefore, the party
organization must have an interest that the voters vote sincerely (so that the
most popular candidates get on the top of the party list) even when it is clear
to the individual voter that he wastes a part of his vote when he votes for a
candidate who is certain to win one of the first 50 places of the party list
even without one’s vote.
Suppose that the top-down approach is being used and that the first k–1
places have already been filled. Suppose Hk is the set of all those sets (each
of k candidates) that each contain all those k–1 candidates who have already
got a place in this party list. Suppose there is a feasible path from set A ∈ Hk
to set B ∈ Hk and no feasible path from set B to set A. Then, when we want
that the used method to fill the k-th place is not needlessly vulnerable to
Hylland free riding and vote management, then B ∉ k. In section 7.1, we
propose a method that satisfies this criterion.
43
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
7.1. Definition of the Schulze Proportional Ranking Method
In this section, we propose new proportional ranking method, where the
vulnerability to Hylland free riding and vote management is minimized.
Stage 1:
Proportional completion is used to complete V to W.
Suppose NW is the number of voters in W.
Suppose ρ(w) ∈  with ρ(w) > 0 is the weight of voter w ∈ W.
Stage 2:
For k : = 1 to (C–1) do
{
Suppose d1,...,dk–1 are already elected.
Hk ⊂ Ak is the set of all those sets (each of k candidates) that each
contain all elected candidates.
A path from set X ∈ Hk to set Y ∈ Hk is a sequence of sets
C(1),...,C(n) ∈ Hk with the following properties:
1.
2.
3.
4.
X ≡ C(1).
Y ≡ C(n).
2 ≤ n < ∞.
For all i = 1,...,(n–1): C(i) and C(i+1) differ in exactly one
candidate. That means: | C(i) ∩ C(i+1) | = k – 1 and
| C(i) ∪ C(i+1) | = k + 1.
Suppose a,b ∈ A. Then N[{d1,...,dk–1,a},b] ∈  is the largest value
such that there is a t ∈ (NW×k) such that
(7.1.1)
∀ i ∈ {1,...,NW} ∀ j ∈ {1,...,k}: tij ≥ 0.
(7.1.2)
∀ i ∈ {1,...,NW}:
∑t
k
ij
≤ ρ(i).
j =1
(7.1.3a)
∀ i ∈ {1,...,NW} ∀ j ∈ {1,...,(k–1)}: b i dj ⇒ tij = 0.
(7.1.3b)
∀ i ∈ {1,...,NW}: b i a ⇒ tik = 0.
(7.1.4)
∀ j ∈ {1,...,k}:
NW
∑t
ij
≥ N[{d1,...,dk–1,a},b].
i =1
If X,Y ∈ Ak differ in exactly one candidate, then we define Ñ[X,Y] : =
N[{d1,...,dk–1,a},b] with X = {d1,...,dk–1,a} and b = Y \ X.
44
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
The strength of the path C(1),...,C(n) is
min { Ñ[C(i),C(i+1)] | i = 1,...,(n–1) }.
In other words: The strength of a path is the strength of its weakest link.
P[A,B] : = max { min { Ñ[C(i),C(i+1)] | i = 1,...,(n–1) }
| C(1),...,C(n) is a path from set A to set B }.
In other words: P[A,B] is the strength of the strongest path from set
A ∈ Hk to set B ∈ Hk \ {A}.
(7.1.5)
The binary relation k on Hk is defined as follows:
AB ∈ k : ⇔ P[A,B] > P[B,A].
(7.1.6)
k : = { A ∈ Hk | ∀ B ∈ Hk \ {A}: BA ∉ k } is the set of
winning sets.
Candidate a ∈ A is eligible if and only if (1) a ∉ {d1,...,dk–1} and
(2) a ∈ A for an A ∈ k. The k-th place goes to an eligible candidate
a ∈ A with ba ∉ 1 for every other eligible candidate b.
}
45
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
7.2. Example
Example ( C = 5 candidates; N = 504 voters ):
6
72
12
6
30
48
24
168
108
30
voters
voters
voters
voters
voters
voters
voters
voters
voters
voters
a v d v b v c v e
a v d v e v b v c
a v d v e v c v b
a v e v b v d v c
b v d v c v e v a
b v e v a v d v c
b v e v d v c v a
c v a v e v b v d
d v b v e v c v a
e v a v b v d v c
Step 1:
k = 1.
H1 = { {a}, {b}, {c}, {d}, {e} }.
Ñ[*,{a}]
Ñ[*,{b}]
Ñ[*,{c}]
Ñ[*,{d}]
Ñ[*,{e}]
Ñ[{a},*]
---
294
174
342
264
Ñ[{b},*]
210
---
324
306
216
Ñ[{c},*]
330
180
---
168
204
Ñ[{d},*]
162
198
336
---
228
Ñ[{e},*]
240
288
300
276
---
... to a
... to b
... to c
... to d
... to e
from a ...
---
a, 294, b
a, 342, d,
336, c
a, 342, d
a, 264, e
from b ...
b, 324, c,
330, a
---
b, 324, c
b, 324, c,
330, a,
342, d
b, 324, c,
330, a,
264, e
from c ...
c, 330, a
c, 330, a,
294, b
---
c, 330, a,
342, d
c, 330, a,
264, e
from d ...
d, 336, c,
330, a
d, 336, c
---
d, 336, c,
330, a,
264, e
from e ...
e, 300, c,
330, a
e, 300, c
e, 300, c,
330, a,
342, d
---
The strongest paths are:
d, 336, c,
330, a,
294, b
e, 300, c,
330, a,
294, b
46
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Candidate e is the unique winner, since candidate e is the unique
candidate with P[e,x] ≥ P[x,e] for every other candidate x. Therefore,
candidate e gets the first place of the proportional ranking.
Step 2:
k = 2.
H2 = { {a,e}, {b,e}, {c,e}, {d,e} }.
Ñ[*,{ae}]
Ñ[*,{be}]
Ñ[*,{ce}]
Ñ[*,{de}]
Ñ[{ae},*]
---
147
153
183
Ñ[{be},*]
120
---
168
153
Ñ[{ce},*]
204
144
---
138
Ñ[{de},*]
120
198
168
---
... to ae
... to be
... to ce
... to de
from ae ...
---
ae, 183, de,
198, be
ae, 183, de,
168, ce
ae, 183, de
from be ...
be, 168, ce,
204, ae
---
be, 168, ce
be, 168, ce,
204, ae,
183, de
from ce ...
ce, 204, ae
ce, 204, ae,
183, de,
198, be
---
ce, 204, ae,
183, de
from de ...
de, 168, ce,
204, ae
de, 198, be
de, 168, ce
---
The strongest paths are:
Set {c,e} is the unique winning set, since set {c,e} is the unique set
with P[{c,e},B] ≥ P[B,{c,e}] for every other set B ∈ H2. Therefore,
candidate c gets the second place of the proportional ranking.
Step 3:
k = 3.
H3 = { {a,c,e}, {b,c,e}, {c,d,e} }.
47
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Ñ[*,{ace}]
Ñ[*,{bce}]
Ñ[*,{cde}]
Ñ[{ace},*]
---
98
122
Ñ[{bce},*]
120
---
102
Ñ[{cde},*]
120
134
---
... to ace
... to bce
... to cde
from ace ...
---
ace, 122, cde,
134, bce
ace, 122, cde
from bce ...
bce, 120, ace
---
bce, 120, ace,
122, cde
from cde ...
cde, 120, ace
cde, 134, bce
---
The strongest paths are:
Set {a,c,e} is the unique winning set, since set {a,c,e} is the unique
set with P[{a,c,e},B] ≥ P[B,{a,c,e}] for every other set B ∈ H3.
Therefore, candidate a gets the third place of the proportional ranking.
Step 4:
k = 4.
H4 = { {a,b,c,e}, {a,c,d,e} }.
Ñ[*,{abce}]
Ñ[*,{acde}]
Ñ[{abce},*]
---
99
Ñ[{acde},*]
98
---
The strongest paths are:
... to abce
... to acde
from abce ...
---
abce, 99, acde
from acde ...
acde, 98, abce
---
Set {a,b,c,e} is the unique winning set, since set {a,b,c,e} is the
unique set with P[{a,b,c,e},B] ≥ P[B,{a,b,c,e}] for every other set
B ∈ H4. Therefore, candidate b gets the fourth place of the
proportional ranking.
Therefore, the final proportional ranking is e  c  a  b  d.
48
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
8. Database
We applied the Schulze STV method and the Schulze proportional
ranking method to the instances of Tideman’s (2000, 2006) database. This
database consists of 66 instances. Only in 3 of the 66 instances of Tideman’s
database (A10, A13, A34), the winning set of the Schulze STV method
differs from the first M candidates of the Schulze proportional ranking. In 19
instances, the winning set of the Schulze STV method differs from the
winning set of traditional STV methods. Table 8.1 lists all these instances.
1
2
3
4
name N
C M
A04
A05
A06
A07
14
16
9
17
43
762
280
79
2
7
5
2
5 A10 83 19 3
6
7
8
9
A11 963 10 6
A13 104 26 2
A15 77 21 2
A33 9 18 3
10 A34 63 14 12
11
12
13
14
15
A35
A53
A55
A59
A65
176
460
302
694
198
17
10
10
7
10
5
4
5
4
6
16 A67 183 14 10
17
18
19
20
A71
A74
A79
A80
500
253
362
269
8
3
8
7
7
2
4
5
21 A90 366 20 12
Schulze
proportional
ranking
i a ...
ai
ik
ik
ai
a c d e g k m a c d e g k m a c d e g k m a c d e g l m a c m e d g l ...
i h e c b ...
cefhi
cefhi
cefhi
bcehi
i d ...
ci
ci
ci
di
( n a p ... ) or
mnp
mnp
mnp
mnp
( n m p ... )
a c h e j d ...
aceghi
aceghi
aceghi
acdehj
kt
i t ...
kt
kt
kt
l r ...
lr
il
il
lr
o e n ...
[1]
[1]
[1]
eno
jbhenkl
abcdef
abcdef
abcdef
abcdef
m c a d f ...
hjklmn
hjklmn
hjklmn
ghjkmn
f e a q d ...
aefnq
aefkn
aefkn
adefq
j a g f ...
abgj
adgj
afgj
afgj
i a f j e ...
adfij
adefi
adefi
aefij
f d e g ...
bdfg
bdfg
bdfg
defg
g b f e j a ...
bdefgj
bdefgj
bdefgj
abefgj
(fgkbiejlc
bcdef
bcdef
bcdef
bcefg
h ... ) or ( g f k
gijkl
ghijk
gijkl
hijkl
b i e j l c h ... )
a b c d e g h a b c d e g h a b c d e g h a b c d e f g d g c e a b f ...
a c ...
ab
ab
ab
ac
g a e c ...
aefg
adeg
adeg
aceg
a e c g b ...
abcef
abcef
abcef
abceg
aitlecf
abcdef
abcdef
abcdef
abcdef
d s n o b ...
iklnst
iklnst
ilnost
ilnost
NewlandBritton
Meek
Warren
Schulze
STV
Table 8.1: Schulze STV method and Schulze proportional ranking method
compared to the Newland-Britton (1997) method, the Meek (1969, 1970; Hill,
1987) method, and the Warren (1994) method
[1] In instance A33, 10 candidates receive no first preferences, 7 candidates
receive one first preference each, and one candidate receives two first
preferences. The winning sets of the Newland-Britton method, the Meek
method, and the Warren method depend on which candidates happen to be
eliminated by random choice.
49
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
9. Conclusions
A Hylland free rider is a voter who tries to maximize the influence of his
vote by omitting in his individual ranking completely all those candidates
who are certain to be elected. Vote management is a strategy where a party or
a group of independent candidates asks its supporters to vote preferably for
those of its candidates who are less assure of election.
In this paper, we demonstrated that today Hylland free riding (section 3.2)
and all types of vote management (section 4) are the two most serious
problems of proportional representation by the single transferable vote
(STV). We introduced a mathematical concept to describe Hylland free riding
and vote management (section 6.1) and introduced an STV method (section
6.2) and a method to produce party lists (section 7) where the vulnerability to
these strategies is minimized ( i.e. methods that are vulnerable to these
strategies only in those cases in which otherwise Droop proportionality
would have to be violated ).
The single-winner case of the proposed methods has already been
analyzed by Schulze (2011). Because of the large number of satisfied
criteria, both in the single-winner case and in the multi-winner case, we
consider the proposed methods to be good methods for public elections.
References
Amy DJ (1993), “Real Choices / New Voices”, Columbia University Press,
New York
Anderson DM (1995), “PR in Toledo: The Neglected Stepchild of Municipal
Reform”, Barber (1995): 241–281
Bakker EA, Lijphart A (1980), “A Crucial Test of Alphabetic Voting: The
Elections at the University of Leiden, 1973–1978”, British Journal of
Political Science 10: 521–525
Barber KL (1995), “Proportional Representation and Election Reform in
Ohio”, Ohio State University Press, Columbus
Bartholdi JJ, Orlin JB (1991), “Single transferable vote resists strategic
voting”, Social Choice and Welfare 8: 341–354
Bax M (1973), “Harpstrings and Confessions”, doctoral dissertation,
University of Amsterdam
Bentley H (1926), “Cincinnati’s Right About Face in Government”, National
Municipal Review 15: 465–473
Berger TR (2004), “A City of Neighbourhoods: Report of the 2004
Vancouver Electoral Reform Commission”
Bowler S, Farrell DM (1991a), “Party Loyalties in Complex Settings: STV
and Party Identification”, Political Studies 39: 350–362
Bowler S, Farrell DM (1991b), “Voter Behaviour under Proportional
Representation by the Single Transferable Vote: Solving the Puzzle of the
Irish Party System”, Manchester Papers in Politics
Bowler S, Grofman B (2000a), “STV’s Place in the Family of Electoral
Systems”, Bowler (2000b): 265–270
Bowler S, Grofman B (2000b), “Elections in Australia, Ireland, and Malta
under the single transferable vote”, University of Michigan Press, Ann
Arbor
Bowler S, Donovan T, Brockington D (2003), “Electoral Reform and
Minority Representation: Local Experiments with Alternative Elections”,
Ohio State University Press
50
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Brams SJ, Fishburn PC (1984), “Some Logical Defects of the Single
Transferable Vote”, Lijphart (1984): 147–151
Brams SJ, Taylor AD (1996), “Fair Division”, Cambridge University Press
Braunias K (1932), “Das parlamentarische Wahlrecht — Ein Handbuch über
die Bildung der gesetzgebenden Körperschaften in Europa”, Beiträge zum
ausländischen Recht und Völkerrecht 18–18a
Burnham RA (1990), “‘Pulling Together’ for Pluralism: Politics, Planning,
and Government in Cincinnati, 1924–1959”, University of Cincinnati
Burnham RA (1997), “Reform, politics, and race in Cincinnati: Proportional
representation and the City Charter Committee, 1924–1959”, Journal of
Urban History 23: 131–163
Busch RJ (1995), “Ashtabula: The Pioneer Community”, Barber (1995): 83–
115
Busteed MA (1990), “Voting Behaviour in the Republic of Ireland”,
Clarendon Press, Oxford
Chen S (1994), “The Irish Single Transferable Vote System and Ballot
Position Effects”, University of New Orleans
Cohan AS, McKinlay RD, Mughan A (1975), “The Used Vote and Electoral
Outcomes: The Irish General Election of 1973”, British Journal of
Political Science 5: 363–383
Cohan AS, McKinlay RD (1978), “The Used Vote and Electoral Outcomes:
The Irish General Election of 1977”, British Journal of Political Science
8: 492–498
Condorcet MJAN (1785), “Essai sur l’application de l’analyse à la
probabilité des décisions rendues à la pluralité des voix”, Imprimerie
Royale, Paris
Cox GW (1997), “Making Votes Count”, Cambridge University Press
Darcy R, McAllister I (1990), “Ballot Position Effects”, Electoral Studies 9:
5–17
Darcy R, Mackerras M (1993), “Rotation of Ballots: Minimizing the
Number of Rotations”, Electoral Studies 12: 77–82
Doron G, Kronick R (1977), “Single Transferable Vote: An Example of a
Perverse Social Choice Function”, American Journal of Political Science
21: 303–311
Droop HR (1881), “On Methods of Electing Representatives”, Journal of the
Statistical Society of London 44: 141–202
Dummett MAE (1984), “Voting Procedures”, Clarendon Press, Oxford
Dummett MAE (1997), “Principles of Electoral Reform”, Oxford University
Press
Farrell DM (1992), “Ireland”, Katz (1992): 389–457
Farrell DM (1993), “Campaign strategies”, (Gallagher, 1993b): 21–38
Farrell DM, Mackerras M, McAllister I (1996), “Designing Electoral
Institutions: STV Systems and their Consequences”, Political Studies 44:
24–43
Farrell DM, McAllister I (2000), “Through a Glass Darkly: Understanding
the World of STV”, Bowler (2000b): 17–36
Farrell DM, McAllister I (2006), “The Australian Electoral System”,
University of New South Wales Press, Sydney, 2006
Fennell RJC (1994), “Is a feedback method of calculating the quota really
necessary?”, Voting Matters 2: 9–11
Gallagher M (1980), “Candidate Selection in Ireland: The Impact of
Localism and the Electoral System”, British Journal of Political Science
10: 489–503
Gallagher M (1988a), “Ireland: the increasing role of the centre”, (Gallagher,
1988b): 119–144
51
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Gallagher M, Marsh M (1988b), “Candidate Selection in Comparative
Perspective”, SAGE Publications
Gallagher M (1990a), “The election results and the new Dáil”, Gallagher
(1990b): 68–93
Gallagher M, Sinnott R (1990b), “How Ireland Voted 1989”, UC Galway
Press
Gallagher M (1992), “Comparing Proportional Representation Electoral
Systems: Quotas, Thresholds, Paradoxes and Majorities”, British Journal
of Political Science 22: 469–496
Gallagher M (1993a), “The election of the 27th Dáil”, (Gallagher, 1993b):
57–78
Gallagher M, Laver M (1993b), “How Ireland Voted 1992”, Folens and
PSAI Press, Dublin & Limerick
Gallagher M (1999), “The Results Analysed”, (Marsh, 1999): 121–150
Gallagher M (2003a), “Analysis of the Results”, (Gallagher, 2003b): 88–118
Gallagher M, Marsh M, Mitchell P (2003b), “How Ireland Voted 2002”,
Palgrave Macmillan
Gallagher M (2008a), “The Earthquake that Never Happened: Analysis of
the Results”, (Gallagher, 2008b): 78–104
Gallagher M, Marsh M (2008b), “How Ireland Voted 2007”, Palgrave
Macmillan
Galligan Y (1999), “Candidate Selection”, (Marsh, 1999): 57–81
Garvin T (1976), “Local Party Activists in Dublin: Socialization, Recruitment
and Incentives”, British Journal of Political Science 6: 369–380
Goldman RP (1930), “An Analysis of Cincinnati’s Proportional
Representation Elections”, American Political Science Review 24: 699–
710
Gosnell HF (1930), “Motives for Voting as Shown by the Cincinnati P.R.
Election of 1929”, National Municipal Review 19: 471–476
Grofman B, Lijphart A (1986), “Electoral Laws and Their Political
Consequences”, Agathon Press, New York
Grofman B, Lee SC, Winkler E, Woodall B (1999), “Elections in Japan,
Korea, and Taiwan under the Single Non-Transferable Vote”, University
of Michigan Press, Ann Arbor
Hallett GH (1941), “New York’s Third PR Election”, National Municipal
Review 30: 731–736
Hallett GH (1946), “PR in New York Prevents Landslide”, National
Municipal Review 35: 44–47
Harris JP (1930), “Practical Workings of Proportional Representation in the
United States and Canada”, National Municipal Review 19: 337–383
Hatton AR (1920), “The Second Proportional Representation Election in
Kalamazoo”, National Municipal Review 9: 84–92
Herbert S (2003), “The Single Transferable Vote in Practice”, SPICe
Briefing
Hermens FA (1968), “Demokratie oder Anarchie?”, Westdeutscher Verlag,
Köln/Cologne
Hill ID, Wichmann BA, Woodall DR (1987), “Algorithm 123 — The Single
Transferable Vote by Meek’s Method”, Computer Journal 30: 277–281
Hill ID (1994), “Are better STV rules worthwhile? — A reply to RJC
Fennell”, Voting Matters 3: 6–8
Hill ID (1995), “Trying to find a winning set of candidates”, Voting Matters
4: 3
Hill ID (1998), “STV with constraints”, Voting Matters 9: 2–4
Hill ID (1999), “Response by ID Hill”, Voting Matters 10: 4
Hoag CG, Hallett GH (1926), “Proportional Representation”, MacMillan
Company, New York
52
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Holmes M (1999), “Organisational Preparation and Political Marketing”,
(Marsh, 1999): 29–56
Hughes CA (2000), “STV in Australia”, (Bowler, 2000b): 155–177
Hylland A (1992), “Proportional Representation without Party Lists”,
(Malnes, 1992): 126–153
Johnston JP, Koene M (2000), “Learning History’s Lessons Anew: The Use
of STV in Canadian Municipal Elections”, (Bowler, 2000b): 205–247
Katz RS (1981), “But How Many Candidates Should We Have in Donegal?
Numbers of Nominees and Electoral Efficiency in Ireland”, British
Journal of Political Science 11: 117–122
Katz RS, Mair P (1992), “Party Organizations”, SAGE Publications
Kelley J, McAllister I (1984), “Ballot Paper Cues and the Vote in Australia
and Britain: Alphabetic Voting, Sex, and Title”, Public Opinion
Quarterly 48: 452–466
Kestelman P (2000), “AV-plus, PR and Essential AMS”, Voting Matters 11:
3–5
Kestelman P (2002), “Positional Voting Bias Revisited”, Voting Matters 15:
2–5
Kitchener E (1999), “STV with constraints”, Voting Matters 10: 3–4
Kleinman D (2003), “A quota preferential model for the election of
representative assemblies”, submission to the Citizens’ Assembly on
Electoral Reform in British Columbia
Kolesar RJ (1995), “PR in Cincinnati: From ‘Good Government’ to the
Politics of Inclusion?”, Barber (1995): 160–208
Laver M, Mair P, Sinnott R (1987), “How Ireland Voted 1987”, Poolbeg
Press, Dublin
Laver M (1998), “The Irish General and Presidential Elections of 1997”,
Electoral Studies 17: 567–575
Lijphart A, Irwin GA (1979), “Nomination Strategies in the Irish STV
System: The Dáil Elections of 1969, 1973 and 1977”, British Journal of
Political Science 9: 362–369
Lijphart A, Grofman B (1984), “Choosing an Electoral System”, Praeger,
New York
Lijphart A, López Pintor R, Sone Y (1986), “The Limited Vote and the
Single Nontransferable Vote: Lessons from the Japanese and Spanish
Examples”, (Grofman, 1986): 154–169
Liu IC (1999), “Campaigning in an SNTV System: The Case of the
Kuomintang in Taiwan”, (Grofman, 1999): 181–208
Mair P (1986), “Districting Choices under the Single-Transferable Vote”,
(Grofman, 1986): 288–307
Mair P (1987a), “The Changing Irish Party System: Organisation, Ideology
and Electoral Competition”, Frances Pinter, London
Mair P (1987b), “Party Organization, Vote Management, and Candidate
Selection: Toward the Nationalization of Electoral Strategy in Ireland”,
(Penniman, 1987): 104–130
Malnes R, Underdal A (1992), “Rationality and Institutions”, Scandinavian
University Press, Oslo
Marsh M, Mitchell P (1999), “How Ireland Voted 1997”, Political Studies
Association of Ireland, Westview Press
Marsh M (2000), “Candidate Centred but Party Wrapped: Campaigning in
Ireland under STV”, Bowler (2000b): 114–130
McCaffrey GH (1939), “Municipal Affairs: Proportional Representation in
New York City”, American Political Science Review 33: 841–852
McDaid J, (1993), “On the Campaign Trail”, (Gallagher, 1993b): 39–43
Meek BL (1969), “Une nouvelle approche du scrutin transférable”,
Mathématiques et Sciences Humaines 25: 13–23 [Reprinted (1994) as: “A
53
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
New Approach to the Single Transferable Vote — Part I”, Voting Matters
1: 1–7]
Meek BL (1970), “Une nouvelle approche du scrutin transférable (fin)”,
Mathématiques et Sciences Humaines 29: 33–39 [Reprinted (1994) as: “A
New Approach to the Single Transferable Vote — Part II”, Voting
Matters 1: 7–11]
Moley R (1918), “Representation in Dayton and Ashtabula”, National
Municipal Review 7: 27–35
Moley R (1923), “Proportional Representation in Cleveland”, Political
Science Quarterly 38: 652–669
Moscow W (1967), “What have you done for me lately? The ins and outs of
New York politics”, Prentice-Hall, Englewood Cliffs
Newland RA, Britton FS (1997), “How to conduct an election by the Single
Transferable Vote”, Electoral Reform Society of Great Britain and
Ireland (ERS), 3rd Edition
Nurmi HJ (1997), “It’s not just the Lack of Monotonicity”, Representation
34: 48–52
Otten J (1998), “Ordered List Selection”, Voting Matters 9: 8–9
Otten J (2000), “Ordered List Selection -- revisited”, Voting Matters 12: 2–5
Otten J (2001), “STV with multiple constraints”, Voting Matters 13: 4–7
Parker AJ (1982), “The ‘friends and neighbours’ Voting Effect in the
Galway West Constituency”, Political Geography Quarterly 1: 243–262
Penniman HR, Farrell B (1987), “Ireland at the Polls, 1981, 1982, and
1987”, Duke University Press, Cermak
Pilon DM (1994), “The Drive for Proportional Representation in British
Columbia, 1917–23”, Simon Fraser University, Vancouver
Pitkin J (2001), mail to the Civic Values mailing list in July 2001
Robson C, Walsh B (1974), “The Importance of Positional Voting Bias in
the Irish General Election of 1973”, Political Studies 10: 191–203
Rosenstiel C (1998), “Producing a Party List using STV”, Voting Matters 9:
7–8
Saari DG (1994), “Geometry of Voting”, Springer-Verlag, Berlin
Sacks PM (1970), “Bailiwicks, Locality, and Religion: Three elements in an
Irish Dáil Constituency election”, Economic and Social Review 1: 531–554
Sacks PM (1976), “The Donegal Mafia”, Yale University Press
Schulze M (2011), “A new monotonic, clone-independent, reversal
symmetric, and Condorcet-consistent single-winner election method”,
Social Choice and Welfare 36: 267–303
Schwartz T (1986), “The Logic of Collective Choice”, Columbia University
Press, New York
Shaw F (1954), “The History of the New York City Legislature”, Columbia
University Press, New York
Smith JH (1973), “Aggregation of Preferences with Variable Electorate”,
Econometrica 41: 1027–1041
Sowers DC (1934), “Sixteen Years of PR in Boulder”, National Municipal
Review 23: 27–30
Sternberger D, Vogel B, Nohlen D (1969), “Die Wahl der Parlamente, Band
I: Europa”, Walter de Gruyter Verlag, Berlin
Taft CP (1933), “City Management: The Cincinnati Experiment”, Farrer and
Rinehart, New York
Tideman TN (1995), “The Single Transferable Vote”, Journal of Economic
Perspectives 9: 27–38
Tideman TN, Richardson D (2000), “Better voting methods through
technology: The refinement-manageability trade-off in the single
transferable vote”, Public Choice 103: 13–34
54
Markus Schulze, “Part 2 of 5: Free Riding and Vote Management ...”
Tideman TN (2006), “Collective Decisions and Voting: The Potential for
Public Choice”, Ashgate Publishing
Warren CHE (1994), “Counting in STV Elections”, Voting Matters 1: 12–13
Warren CHE (1999a), “The Handsomely Supported Candidate Ploy”, Voting
Matters 10: 2
Warren CHE (1999b), “An example of ordering elected candidates”, Voting
Matters 10: 3
Weaver L, Blount JL (1995), “Hamilton: PR Defeated by Its Own Success”,
Barber (1995): 209–240
Winters R (2001), http://groups.yahoo.com/group/instantrunoff/message/651
Woodall DR (1983), “Computer counting in STV elections”, Representation
23: 4–6 [Reprinted (1994) in Voting Matters 1: 11–12]
Yates I (1990), “On the Campaign Trail”, Gallagher (1990b): 48–52
Zeller B, Bone HA (1947), “The Repeal of PR in New York City — Ten
Years in Retrospect”, American Political Science Review 42: 1127–1148
55